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1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve

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1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve dscount rate of d. The amount of nterest earned n Bruce s account durng the 11th year s equal to X. The amount of nterest earned n Robbe s account durng the 17th year s also equal to X. Calculate X. (A) 28.0 (B) 31.3 (C) 34.6 (D) 36.7 (E) (# 12, May 2003). Erc deposts X nto a savngs account at tme 0, whch pays nterest at a nomnal rate of, compounded semannually. Mke deposts 2X nto a dfferent savngs account at tme 0, whch pays smple nterest at an annual rate of. Erc and Mke earn the same amount of nterest durng the last 6 months of the 8-th year. Calculate. (A) 9.06% (B) 9.26% (C) 9.46% (D) 9.66% (E) 9.86% 3. (# 50, May 2003). Jeff deposts 10 nto a fund today and 20 ffteen years later. Interest s credted at a nomnal dscount rate of d compounded quarterly for the frst 10 years, and at a nomnal nterest rate of 6% compounded semannually thereafter. The accumulated balance n the fund at the end of 30 years s 100. Calculate d. (A) 4.33% (B) 4.43% (C) 4.53% (D) 4.63% (E) (#25 Sample Test). Bran and Jennfer each take out a loan of X. Jennfer wll repay her loan by makng one payment of 800 at the end of year 10. Bran wll repay hs loan by makng one payment of 1120 at the end of year 10. The nomnal sem-annual rate beng charged to Jennfer s exactly one half the nomnal sem annual rate beng charged to Bran. Calculate X. A. 562 B. 565 C. 568 D. 571 E (#1 May 2003). Bruce deposts 100 nto a bank account. Hs account s credted nterest at a nomnal rate of nterest convertble semannually. At the same tme, Peter deposts 100 nto a separate account. Peter s account s credted nterest at a force of nterest of δ. After 7.25 years, the value of each account s 200. Calculate ( δ). (A) 0.12% (B) 0.23% (C) 0.31% (D) 0.39% (E) 0.47% 6. (#23, Sample Test). At tme 0, deposts of 10, 000 are made nto each of Fund X and Fund Y. Fund X accumulates at an annual effectve nterest rate of 5 %. Fund Y accumulates at a smple nterest rate of 8 %. At tme t, the forces of nterest on the two funds are equal. At tme t, the accumulated value of Fund Y s greater than the accumulated value of Fund X by Z. Determne Z. A B C D E 7. (#24, Sample Test). At a force of nterest δ t = 2 k+2t. () a depost of 75 at tme t = 0 wll accumulate to X at tme t = 3; and () the present value at tme t = 3 of a depost of 150 at tme t = 5 s also equal to X. Calculate X. A. 105 B. 110 C. 115 D. 120 E (# 37, May 2000). A customer s offered an nvestment where nterest s calculated accordng to the followng force of nterest: 0.02t f 0 t 3 δ t = f 3 t The customer nvests 1000 at tme t = 0. What nomnal rate of nterest, compounded quarterly, s earned over the frst four year perod? (A) 3.4% (B) 3.7% (C) 4.0% (D) 4.2% (E) 4.5% 9. (# 53, November 2000). At tme 0, K s deposted nto Fund X, whch accumulates at a force of nterest δ t = 0.006t 2. At tme m, 2K s deposted nto Fund Y, whch accumulates at an annual effectve nterest rate of 10%. At tme n, where n m, the accumulated value of each fund s 4K. Determne m. (A) 1.6 (B) 2.4 (C) 3.8 (D) 5.0 (E) (# 45, May 2001). At tme t = 0, 1 s deposted nto each of Fund X and Fund Y. Fund X accumulates at a force of nterest δ t = t2. Fund Y accumulates at a nomnal rate of k dscount of 8% per annum convertble semannually. At tme t = 5, the accumulated value of Fund X equals the accumulated value of Fund Y. Determne k. (A) 100 (B) 102 (C) 104 (D) 106 (E) (# 49, May 2001). Tawny makes a depost nto a bank account whch credts nterest at a nomnal nterest rate of 10% per annum, convertble semannually. At the same tme, Fabo deposts 1000 nto a dfferent bank account, whch s credted wth smple nterest. At the end of 5 years, the forces of nterest on the two accounts are equal, and Fabo s account has accumulated to Z. Determne Z. (A) 1792 (B) 1953 (C) 2092 (D) 2153 (E) (# 1, May 2000). Joe deposts 10 today and another 30 n fve years nto a fund payng smple nterest of 11% per year. Tna wll make the same two deposts, but the 10 wll be deposted n years from today and the 30 wll be deposted 2n years from today. Tna s deposts earn an annual effectve rate of 9.15%. At the end of 10 years, the accumulated 2 amount of Tna s deposts equals the accumulated amount of Joe s deposts. Calculate n. (A) 2.0 (B) 2.3 (C) 2.6 (D) 2.9 (E) (# 1, November 2001 ). Erne makes deposts of 100 at tme 0, and X at tme 3. The fund grows at a force of nterest δ t = t2, t 0. The amount of nterest earned from tme 3 to 100 tme 6 s X. Calculate X. (A) 385 (B) 485 (C) 585 (D) 685 (E) (# 24, November 2001). Davd can receve one of the followng two payment streams: () 100 at tme 0, 200 at tme n, and 300 at tme 2n () 600 at tme 10 At an annual effectve nterest rate of, the present values of the two streams are equal. Gven ν n = , determne. (A) 3.5% (B) 4.0% (C) 4.5% (D) 5.0% (E) 5.5% 15. (# 17, May 2003). An assocaton had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month durng the year, the assocaton deposted 10 from membershp fees. There were wthdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31. Calculate the dollar weghted rate of return for the year. (A) 9.0% (B) 9.5% (C) 10.0% (D) 10.5% (E) 11.0% 16. (#32, Sample Test). 100 s deposted nto an nvestment account on January 1, You are gven the followng nformaton on nvestment actvty that takes place durng the year: Aprl 19, 1998 October 30, 1998 Value mmedately pror to depost Depost 2X X The amount n the account on January 1, 1999 s 115. Durng 1998, the dollar weghted return s 0% and the tme-weghted return s y. Calculate y. (A) 1.5% (B) 0.7% (C) 0.0% (D) 0.7% (E) 1.5% 17. (# 27, November 2000). An nvestor deposts 50 n an nvestment account on January 1. The followng summarzes the actvty n the account durng the year: Date Value Immedately Before Depost Depost March June October On June 30, the value of the account s On December 31, the value of the account s X. Usng the tme weghted method, the equvalent annual effectve yeld durng the frst 6 months s equal to the (tme-weghted) annual effectve yeld durng the entre 1-year perod. Calculate X. (A) (B) (C) (D) (E) (#31, May 2001). You are gven the followng nformaton about an nvestment account: Date Value Immedately Before Depost Depost January 1 10 July 1 12 X December 31 X Over the year, the tme weghted return s 0%, and the dollar-weghted return s Y. Calculate Y. (A) 25% (B) 10% (C) 0% (D) 10% (E) 25% 19. (#16, May 2000 ). On January 1, 1997, an nvestment account s worth 100, 000. On Aprl 1, 1997, the value has ncreased to 103,000 and 8, 000 s wthdrawn. On January 1, 1999, the account s worth 103, 992. Assumng a dollar weghted method for 1997 and a tme weghted method for 1998, the annual effectve nterest rate was equal to x for both 1997 and Calculate x. (A) 6.00% (B) 6.25% (C) 6.50% (D) 6.75% (E) 7.00% 20. (# 28, November 2001). Payments are made to an account at a contnuous rate of (8k+tk), where 0 t 10. Interest s credted at a force of nterest δ t = 1. After 10 years, the 8+t account s worth 20, 000. Calculate k. (A) 111 (B) 116 (C) 121 (D) 126 (E) (# 2, November, 2000) The followng table shows the annual effectve nterest rates beng credted by an nvestment account, by calendar year of nvestment. The nvestment year method s applcable for the frst 3 years, after whch a portfolo rate s used: Calendar year calendar of orgnal year of Portfolo nvestment Portfolo rate Rate % 10% t% % % 5% 10% 1994 t 1% % t 2% 12% % % 11% 6% % % 7% 10% % 4 An nvestment of 100 s made at the begnnng of years 1990, 1991, and The total amount of nterest credted by the fund durng the year 1993 s equal to Calculate t. (A) 7.00 (B) 7.25 (C) 7.50 (D) 7.75 (E) (# 51, November, 2000) An nvestor deposts 1000 on January 1 of year x and deposts another 1000 on January 1 of year x+2 nto a fund that matures on January 1 of year x+4. The nterest rate on the fund dffers every year and s equal to the annual effectve rate of growth of the gross domestc product (GDP) durng the 4 th quarter of the prevous year. The followng are the relevant GDP values for the past 4 years: Year III Quarter IV Quarter Year Quarter III Quarter III x x x x What s the nternal rate of return earned by the nvestor over the 4 year perod? (A) 1.66% (B) 5.10% (C) 6.15% (D) 6.60% (E) 6.78% 23. (#26, Sample Test). Carol and John shared equally n an nhertance. Usng hs nhertance, John mmedately bought a 10-year annuty-due wth an annual payment of 2500 each. Carol put her nhertance n an nvestment fund earnng an annual effectve nterest rate of 9%. Two years later, Carol bought a 15-year annuty-mmedate wth annual payment of Z. The present value of both annutes was determned usng an annual effectve nterest rate of 8%. Calculate Z. A B C D E (#27, Sample Test). Susan and Jeff each make deposts of 100 at the end of each year for 40 years. Startng at the end of the 41st year, Susan makes annual wthdrawals of X for 15 years and Jeff makes annual wthdrawals of Y for 15 years. Both funds have a balance of 0 after the last wthdrawal. Susan s fund earns an annual effectve nterest rate of 8 %. Jeff s fund earns an annual effectve nterest rate of 10 %. Calculate Y X. A B C D E (# 22, November 2000). Jerry wll make deposts of 450 at the end of each quarter for 10 years. At the end of 15 years, Jerry wll use the fund to make annual payments of Y at the begnnng of each year for 4 years, after whch the fund s exhausted. The annual effectve rate of nterest s 7%. Determne Y. (A) 9573 (B) 9673 (C) 9773 (D) 9873 (E) 26. (# 27, November 2001). A man turns 40 today and wshes to provde supplemental retrement ncome of 3000 at the begnnng of each month startng on hs 65th brthday. Startng today, he makes monthly contrbutons of X to a fund for 25 years. The fund earns a nomnal rate of 8% compounded monthly. Each 1000 wll provde for 9.65 of ncome at the begnnng of each month startng on hs 65th brthday untl the end of hs lfe. Calculate X. (A) (B) (C) (D) (E) (# 47, May 2000). Jm began savng money for hs retrement by makng monthly deposts of 200 nto a fund earnng 6% nterest compounded monthly. The frst depost occurred on January 1, Jm became unemployed and mssed makng deposts 60 through 72. He then contnued makng monthly deposts of 200. How much dd Jm accumulate n hs fund on December 31, 1999? (A) 53, 572 (B) 53, 715 (C) 53, 840 (D) 53, 966 (E) 54, (# 12, November 2001). To accumulate 8000 at the end of 3n years, deposts of 98 are made at the end of each of the frst n years and 196 at the end of each of the next 2n years. The annual effectve rate of nterest s. You are gven (l + ) n = 2.0. Determne. (A) 11.25% (B) 11.75% (C) 12.25% (D) 12.75% (E) 13.25% 29. (# 34, November 2000). Chuck needs to purchase an tem n 10 years. The tem costs 200 today, but ts prce nflates 4% per year. To fnance the purchase, Chuck deposts 20 nto an account at the begnnng of each year for 6 years. He deposts an addtonal X at the begnnng of years 4, 5, and 6 to meet hs goal. The annual effectve nterest rate s 10%. Calculate X. (A) 7.4 (B) 7.9 (C) 8.4 (D) 8.9 (E) (# 8, May 2003). Kathryn deposts 100 nto an account at the begnnng of each 4 year perod for 40 years. The account credts nterest at an annual effectve nterest rate of. The accumulated amount n the account at the end of 40 years s X, whch s 5 tmes the accumulated amount n the account at the end of 20 years. Calculate X. (A) 4695 (B) 5070 (C) 5445 (D) 5820 (E) (# 33, May 2003). At an annual effectve nterest rate of, 0, both of the followng annutes have a present value of X: () a 20 year annuty mmedate wth annual payments of 55 () a 30 year annuty mmedate wth annual payments that pays 30 per year for the frst 10 years, 60 per year for the second 10 years, and 90 per year for the fnal 10 years Calculate X. (A) 575 (B) 585 (C) 595 (D) 605 (E) 615 6 32. (# 17, May 2001). At an annual effectve nterest rate of, 0%, the present value of a perpetuty payng 10 at the end of each 3 year perod, wth the frst payment at the end of year 6, s 32. At the same annual effectve rate of, the present value of a perpetuty mmedate payng 1 at the end of each 4-month perod s X. Calculate X. (A) 38.8 (B) 39.8 (C) 40.8 (D) 41.8 (E) (# 5, May 2001). A perpetuty mmedate pays X per year. Bran receves the frst n payments, Colleen receves the next n payments, and Jeff receves the remanng payments. Bran s share of the present value of the orgnal perpetuty s 40%, and Jeff s share s K. Calculate K. (A) 24% (B) 28% (C) 32% (D) 36% (E) 40% 34. (# 50, May 2001). The present values of the followng three annutes are equal: () perpetuty mmedate payng 1 each year, calculated at an annual effectve nterest rate of 7.25% () 50 year annuty-mmedate payng 1 each year, calculated at an annual effectve nterest rate of j% () n year annuty-mmedate payng 1 each year, calculated at an annual effectve nterest rate of j 1% Calculate n. (A) 30 (B) 33 (C) 36 (D) 39 (E) (# 14, May 2000). A perpetuty payng 1 at the begnnng of each 6 month perod has a present value of 20. A second perpetuty pays X at the begnnng of every 2 years. Assumng the same annual effectve nterest rate, the two present values are equal. Determne X. (A) 3.5 (B) 3.6 (C) 3.7 (D) 3.8 (E) (#29, Sample Test). Chrs makes annual deposts nto a bank account at the begnnng of each year for 20 years. Chrs ntal depost s equal to 100, wth each subsequent depost k% greater than the prevous year s depost. The bank credts nterest at an annual effectve rate of 5%. At the end of 20 years, the accumulated amount n Chrs account s equal to Gven k 5, calculate k. A B C D E (# 5, November 2001). Mke buys a perpetuty mmedate wth varyng annual payments. Durng the frst 5 years, the payment s constant and equal to 10. Begnnng n year 6, the payments start to ncrease. For year 6 and all future years, the current year s payment s K% larger than the prevous year s payment. At an annual effectve nterest rate of 9.2%, the perpetuty has a present value of Calculate K, gven K 9.2. (A) 4.0 (B) 4.2 (C) 4.4 (D) 4.6 (E) 4.8 7 38. (# 9, May 2000). A senor executve s offered a buyout package by hs company that wll pay hm a monthly beneft for the next 20 years. Monthly benefts wll reman constant wthn each of the 20 years. At the end of each 12-month perod, the monthly benefts wll be adjusted upwards to reflect the percentage ncrease n the CPI. You are gven: () The frst monthly beneft s R and wll be pad one month from today. () The CPI ncreases 3.2% per year forever. At an annual effectve nterest rate of 6%, the buyout package has a value of 100, 000. Calculate R. (A) 517 (B) 538 (C) 540 (D) 548 (E) (# 45, May 2003). A perpetuty-mmedate pays 100 per year. Immedately after the ffth payment, the perpetuty s exchanged for a 25 year annuty mmedate that wll pay X at the end of the frst year. Each subsequent annual payment wll be 8% greater than the precedng payment. Immedately after the 10th payment of the 25 year annuty, the annuty wll be exchanged for a perpetuty-mmedate payng Y per year. The annual effectve rate of nterest s 8%. Calculate Y. (A) 110 (B) 120 (C) 130 (D) 140 (E) (# 51, May 2000). Seth deposts X n an account today n order to fund hs retrement. He would lke to receve payments of 50 per year, n real terms, at the end of each year for a total of 12 years, wth the frst payment occurrng seven years from now. The nflaton rate wll be 0.0% for the next sx years and 1.2% per annum thereafter. The annual effectve rate of return s 6.3%. Calculate X. (A) 303 (B) 306 (C) 316 (D) 327 (E) (# 22, May 2003). A perpetuty costs 77.1 and makes annual payments at the end of the year. The perpetuty pays 1 at the end of year 2, 2 at the end of year 3,... n at the end of year (n + 1). After year (n + 1), the payments reman constant at n. The annual effectve nterest rate s 10.5%. Calculate n. (A) 17 (B) 18 (C) 19 (D) 20 (E) (# 16, November 2001). Olga buys a 5 year ncreasng annuty for X. Olga wll receve 2 at the end of the frst month, 4 at the end of the second month, and for each month thereafter the payment ncreases by 2. The nomnal nterest rate s 9% convertble quarterly. Calculate X. (A) 2680 (B) 2730 (C) 2780 (D) 2830 (E) (# 26, May 2000). Betty borrows 19,800 from Bank X. Betty repays the loan by makng 36 equal payments of prncpal at the end of each month. She also pays nterest on the unpad 8 balance each month at a nomnal rate of 12%, compounded monthly. Immedately after the 16th payment s made, Bank X sells the rghts to future payments to Bank Y. Bank Y wshes to yeld a nomnal rate of 14%, compounded sem-annually, on ts nvestment. What prce does Bank X receve? (A) 9,792 (B) 10,823 (C) 10,857 (D) 11,671 (E) 11, (# 44, November 2000). Joe can purchase one of two annutes: Annuty 1: A 10 year decreasng annuty mmedate, wth annual payments of 10, 9, 8,..., 1. Annuty 2: A perpetuty mmedate wth annual payments. The perpetuty pays 1 n year 1, 2 n year 2, 3 n year 3,..., and 11 n year 11. After year 11, the payments reman constant at 11. At an annual effectve nterest rate of, the present value of Annuty 2 s twce the present value of Annuty 1. Calculate the value of Annuty 1. (A) 36.4 (B) 37.4 (C) 38.4 (D) 39.4 (E) (# 20, November 2000). Sandy purchases a perpetuty mmedate that makes annual payments. The frst payment s 100, and each payment thereafter ncreases by 10. Danny purchases a perpetuty due whch makes annual payments of 180. Usng the same annual effectve nterest rate, 0, the present value of both perpetutes are equal. Calculate. (A) 9.2% (B) 9.7% (C) 10.2% (D) 10.7% (E) 11.2% 46. (# 30, Sample Test). Scott deposts: 1 at the begnnng of each quarter n year 1; 2 at the begnnng of each quarter n year 2; 8 at the begnnng of each quarter n year 8. One quarter after the last depost, Scott wthdraws the accumulated value of the fund and uses t to buy a perpetuty-mmedate wth level payments of X at the end of each year. All calculatons assume a nomnal nterest rate of 10% per annum compounded quarterly. Calculate X. A B C D E (# 7, May 2001). Seth, Jance, and Lor each borrow 5000 for fve years at a nomnal nterest rate of 12%, compounded sem annually. Seth has nterest accumulated over the fve years and pays all the nterest and prncpal n a lump sum at the end of fve years. 9 Jance pays nterest at the end of every sx-month perod as t accrues and the prncpal at the end of fve years. Lor repays her loan wth 10 level payments at the end of every sx-month perod. Calculate the total amount of nterest pad on all three loans. (A) 8718 (B) 8728 (C) 8738 (D) 8748 (E) (#28, Sample Test). A loan of 10, 000 s to be amortzed n 10 annual payments begnnng 6 months after the date of the loan. The frst payment, X, s half as large as the other payments. Interest s calculated at an annual effectve rate of 5% for the frst 4.5 years and 3% thereafter. Determne X. A. 640 B. 648 C. 656 D. 664 E (# 12, November 2002). Kevn takes out a 10 year loan of L, whch he repays by the amortzaton method at an annual effectve nterest rate of. Kevn makes payments of 1000 at the end of each year. The total amount of nterest repad durng the lfe of the loan s also equal to L. Calculate the amount of nterest repad durng the frst year of the loan. (A) 725 (B) 750 (C) 755 (D) 760 (E) (# 37, Sample Test). A loan s beng amortzed by means of level monthly payments at an annual effectve nterest rate of 8%. The amount of prncpal repad n the 12 th payment s 1000 and the amount of prncpal repad n the t th payment s Calculate t. A. 198 B. 204 C. 210 D. 216 E (# 10, May 2000). A bank customer borrows X at an annual effectve rate of 12.5% and makes level payments at the end of each year for n years. () The nterest porton of the fnal payment s () The total prncpal repad as of tme (n 1) s () The prncpal repad n the frst payment s Y. Calculate Y. (A) 470 (B) 480 (C) 490 (D) 500 (E) (# 24, May 2000). A small busness takes

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