- 1 = $ Notice the answer is a bit different from the calculator solution ($1,161,338.43) because we rounded the periodic rate.

Transcription

1 Review Problems Note: Answers are in Appendix B. Solutions are on uture value 1. he average growth rate for stocks over the last 75 years is reported to be about 11%, compounded annually. If your grandmother had invested $500 in the stock market 75 years ago and received the 11% return, what would her investment be worth today? N i PV PM V ,253, V = PV = $500(1.11) 75 = $1,253, ol A, 11%, n = 75: V = $500 2, = $1,253, =V(i, n, PM, PV, Mode) =V(11%, 75, 0, -500, 0) $1,253, Jack Green spends $135 a month on cigarettes and is considering the advantages of kicking the habit. If Jack just turned 19 and deposits the $135 at the end of each month into a savings plan earning 8% compounded monthly, how much will he have in his savings plan at age 70, after his initial deposit? N i PV PM V = = ,161, [ (1 + i) ] V = PM = $1,161, i [ ] = $ Notice the answer is a bit different from the calculator solution ($1,161,338.43) because we rounded the periodic rate. ol B, 0.66%, n = 612: V = $135 8, = $1,161, =V(i, n, PM, PV, Mode) =V(8%/12, 51*12, -135, 0, 0) $1,161, Sinking funds 3. Beth received a promise from her Uncle ed. He promises to give her $50,000 on her 30th birthday, years from now. Uncle ed can earn 8.5% compounded quarterly on his money. What amount can Uncle ed deposit today in a savings plan so that the plan would have the required $50,000 in years? N i PV PM V = = , ,000 PV = V = $50,000 = $28, ( ) 26 ol D, 2.125%, n = 26: PV = $50, = $28, =PV(i, n, PM, V, Mode) =PV(8.5%/4, 6.5*4, 0, 50000, 0) ($28,942.51) 4. Refer to Problem 3. If, instead, Uncle ed elects to make quarterly deposits into the plan (starting in 3 months), what is the required quarterly deposit? N i PV PM V 0-1, V(i) PM = $50,000 (.02125) = = $1, ( ) 26 ol, 2.125%, n = 26: PM = $50, = $1, =PM(i, n, PV, V, Mode) =PM(8.5%/4, 6.5*4, 0, 50000, 0) ($1,460.36) 216 Supplement: Additional VM Applications

2 5. Refer back. If, instead, Uncle ed elects to deposit $10,000 today, what additional quarterly deposit is required? N i PV PM V -10, What $10,000 will grow to: V = PV = $10,000( ) 26 = $17, Additional V required: $50,000 - $17, = $32, PM needed to accumulate $32,724.37: V(i) PM = $32, (.02125) = = $ ( ) 26 What $10,000 will grow to (ol A, 2.125%, n = 26): V = $10, = $17, Additional V required: $50,000 - $17, = $32, PM needed to accumulate $32, (ol, 2.125%, n = 26): PM = $32, = $ =PM(i, n, PV, V, Mode) =PM(8.5%/4, 6.5*4, , 50000, 0) ($955.78) Annuities 6. You receive an inheritance of $500,000 and deposit it in a savings plan that earns 6.75% compounded monthly. If you want to live off the interest without withdrawing any of the principal, what amount can you withdraw each month? I = PR = $500, % 1 12 = $2, Refer to Problem 6. If you want the plan to last 35 years, how much can you withdraw at the end of each month? N i PV PM V = = ,000 3, PM = PV(i) 1 = $500,000 ( ) = $3, ( ) 420 ol,.5625%, n = 420: PM = $500, = $3, =PM(i, n, PV, V, Mode) =PM(6.75%/12, 35*12, , 0, 0) $3, Refer back. If you withdraw $2,500 at the end of each month, what will the balance be in 25 years? N i PV PM V = , , What $500,000 will grow to: V = PV = $500,000 ( ) 300 = $2,690, he effect a $2,500 monthly withdrawal will have on V: [ (1 + i) ] V = PM i [ ] = $2,500 = ,946, inal balance $ 743, What $500,000 will grow to (ol A,.5625%, n = 300): V = $500, = $2,690, he effect a $2,500 monthly withdrawal will have on V (ol B): V = $2, = -1,946, inal balance $ 743, =V(i, n, PM, PV, Mode) =V(6.75%/12, 25*12, 2500, , 0) $ 743, Review Problems 217

3 Annual percentage yield (APY) 9. In an advertisement, a bank offers ertificates of Deposit (Ds) at 5.75% compounded semiannually. hey state the APY is 5.83%. onfirm the APY. Use an arbitrary $100 deposit. N i PV PM V = V = PV = $100 ( ) 2 = $ ol A, 2.875%, n = 2: V = $ = $ =V(i, n, PM, PV, Mode) =V(5.75%/2, 2, 0, -100, 0) $ Growth rates he ending balance is $105.83, meaning interest is $5.83. hat is the same as earning a 5.83% annual rate. he APY is 5.83%. 10. uition at a local college is currently $2,550 per year. You want your newborn daughter to attend when she turns 18. If tuition rates are expected to increase at an annual rate of 4.5%, what will the annual tuition be at the college 18 years from now? N i PV PM V ,550 5, V = PV = $2,550 (1.045) 18 = $5, ol A, 4.5%, n = 18: V = $2, = $5, =V(i, n, PM, PV, Mode) =V(4.5%, 18, 0, -2550, 0) $5, Present value 11. Suzie s rich aunt promises to give Suzie $100,000 on her 30th birthday, 12 years from now. If money is worth 8.5% compounded annually, what is today s value of her aunt s promise? PV = N i PV PM V , ,000 V = $100,000 = $37, (1.085) 12 ol D, 8.5%, n = 12: PV = $100, = $37, =PV(i, n, PM, V, Mode) =PV(8.5%, 12, 0, , 0) ($37,570.17) 12. You own a manufacturing business and are thinking about purchasing a labor-saving device at a cost of $150,000. he device will last 15 years and save you $1,400 per month in labor costs (assume that savings are realized at the end of each month). You need to earn 11.5% compounded monthly on your money. What is the value of the device? N i PV PM V = = , ,400 [ ] 1- PV = PM 1 i [ ] 1- = $1,400 1 ( ) = $119, ol,.9583%, n = 180: PV = $1, = $119, =PV(i, n, PM, V, Mode) =PV(11.5%/12, 15*12, 1400, 0, 0) ($119,843.54) 218 Supplement: Additional VM Applications

4 13. Refer to Problem 12. On the basis of your answer, should you buy the device? No; the device is worth about $120,000 to you, considerably less than its $150,000 cost. Installment buying 14. You are thinking of buying a sports car, priced at $28,500. You must pay tax and license fees of $2,000. Your bank will loan you $27,500 at 7.2% for 4 years. Determine your monthly payment. N i PV PM V 4 12 = = , PM = PV(i) 1 = $27,500 (.006) = $ (1.006) 48 ol,.60%, n = 48: PV = $27, = $ =PM(i, n, PV, V, Mode) =PM(7.2%/12, 4*12, 27500, 0, 0) ($661.08) 15. Refer to Problem 14. What is your total finance charge? otal of all payments: 48 $ = $31, Subtract loan amount - 27, inance charge (interest portion of payments) $ 4, Refer back. What is the total cost of the car, including finance charges? ost of the purchase: $28,500 + $2,000 tax and license fees $ 30, Add finance charges (from previous problem) + 4, otal cost, including finance charges $34, You buy a motorcycle on July 1 for $1,500 with $500 down. You agree to pay the seller the remaining $1,000 at 9% with four monthly payments. he first payment is due August 1. alculate the monthly payment. N i PV PM V = , PM = PV(i) 1 = = $ $1,000 (.0075) 1 (1.0075) 4 ol,.75%, n = 4: PV = $1, = $ =PM(i, n, PV, V, Mode) =PM(9%/12, 4, 1000, 0, 0) ($254.71) Review Problems 219

5 18. Refer to Problem 17. alculate interest, principal, and remaining balance for each payment using the U.S. Rule. Payment dates are shown in the table. Remember, the final payment may be slightly different because of rounding and actual payment date. Due date Date received otal payment Interest Principal Balance July 1 (Start) $1, Aug. 1 July 28 $ $6.66 $ $ Sep. 1 Aug. 29 $ $5.93 $ $ Oct. 1 Sep. 27 $ $3.60 $ $ Nov. 1 Nov. 1 $ $2.18 $ $0.00 Procedure for August 1 payment Number of days: 28 = 27 Interest: I = PR = $1,000 9% = $6.66 Principal: $ $6.66 = $ New balance: $1,000 - $ = $ Procedure for November 1 payment Number of days: 3 days in Sep days in Oct. + 1 day in Nov. = 35 Interest: I = PR = $ % = $2.18 Principal: $ (previous balance) otal payment: $ $ = $ Home ownership and mortgage loans 19. You need a $150,000 mortgage loan but are unsure whether to get a % 30-year loan or a % 15-year loan. What is the monthly payment on the 30-year loan? N i PV PM V = = ,000-1, PM = PV(i) 1 = $150,000 ( ) = $1, ( ) 360 ol, %, n = 360: PM = $150, = $1, =PM(i, n, PV, V, Mode) =PM(9.875%/12, 30*12, , 0, 0) ($1,302.52) 20. Refer to Problem 19. What is the monthly payment on the 15-year loan? N i PV PM V = = ,000-1, PM = PV(i) 1 = = $1, $150,000 ( ) 1 ( ) 180 ol,.78125%, n = 180: PM = $150, = $1, =PM(i, n, PV, V, Mode) =PM(9.375%/12, 15*12, , 0, 0) ($1,555.04) 21. Refer back. How much more per month will you pay with the 15-year loan? $1, $1, = $ Refer back. ind the total amount of interest for each loan. 30-year loan: 360 $1, = $468,907.20; $468, $150,000 = $ year loan: 180 $1, = $279,907.20; $279, $150,000 = $129, Supplement: Additional VM Applications

6 23. Refer back. How much more interest will you pay with the 30-year loan? $318, $129, = $189, Refer back. Assume that you get the 15-year loan. Property taxes are currently $2,622 per year and insurance is currently $845 per year. What additional amount is required each month for taxes and insurance (I)? Property taxes $2,622 Insurance otal $3, = $ Refer back. What will your total monthly payment be (PII)? $1, (PI) + $ (I) = $1, (PII) 26. You get a $120,000 mortgage loan at 6% interest, with a monthly payment (PI) of $ alculate interest, principal, and remaining balance for the first monthly payment. Payment number Payment (PI) Interest Principal Balance New loan $120, $ $ $ $119, Step 1 I = PR = $120,000 6% 1 12 = $ Step 2 Principal = $ $ = $ Step 3 Balance = $120, $ = $119, Practice est 1. You deposit $200 today into a savings plan and deposit an additional $25 each month (starting in 1 month) for 22 years. If you earn 6.5% compounded monthly, what will your balance be in 22 years? N i PV PM V = = , V for $200 initial deposit: V = PV = $200 ( ) 264 = $ V for $25 monthly deposit: [ (1 + i) ] V = PM i [ ] = $25 = , otal V $15, V for $200 initial deposit (ol A,.5416%, n = 264): $ = $ V for $25 monthly deposit (ol B,.5416%, n = 264): $ = + 14, otal V $15, =V(i, n, PM, PV, Mode) =V(6.5%/12, 22*12, -25, -200, 0) $15, Practice est 221

7 2. Your uncle dies and your 62-year-old aunt receives $250,000 life insurance proceeds. She needs monthly income and expects to live until she is 90 years old. If she invests the insurance money, earning 7.75% compounded monthly, how much can she withdraw at the end of each month for the next 28 years? N i PV PM V = = ,000 1, PM = PV(i) 1 = $250,000 ( ) = $1, ( ) 336 ol,.64583%, n = 336: PM = $250, = $1, =PM(i, n, PV, V, Mode) =PM(7.75%/12, 28*12, , 0, 0) $1, What is the APY (to the nearest hundreth of a percent) for 6% compounded quarterly? Use an arbitrary $100 deposit. N i PV PM V = V = PV = $100 (1.015) 4 = $ ol A, 1.5%, n = 4: V = $ = $ =V(i, n, PM, PV, Mode) =V(6%/4, 4, 0, -100, 0) $ he ending balance is $106.14, meaning interest is $6.14. hat is the same as earning a 6.14% annual rate. he APY is 6.14%. 4. What is the present value of $25,000 to be received in 5 years, assuming money is worth 8% compounded annually? PV = N i PV PM V , ,000 V = $25,000 = $17, (1.08) 5 ol D, 8%, n = 5: PV = $25, = $17, =PV(i, n, PM, V, Mode) =PV(8%, 5, 0, 25000, 0) ($17,014.58) 5. You buy a truck for $22,200. You must also pay tax and license fees of $1,500. You borrow $20,000 at 6% interest for 5 years with monthly payments. What is the total cost of the truck, including tax and license fees and finance charges? N i PV PM V 5 12 = = , PM = PV(i) 1 = = $ $20,000 (.005) 1 (1.005) 60 ol,.50%, n = 60: PM = $20, = $ =PM(i, n, PV, V, Mode) =PM(6%/12, 5*12, 20000, 0, 0) ($386.66) inance charge Step 1 otal of all payments: 60 $ (above) $23, Step 2 Less loan amount - 20, Interest portion of payments $ 3, otal cost Step 1 ost of the purchase: $22,200 + $1,500 tax and license $23, Step 2 Add finance charge (above) + 3, otal cost $26, Supplement: Additional VM Applications

8 6. On May 24, Whitney Nickle made a payment on her 7.9% car loan. After making the payment, the balance was $1, Whitney got her income tax refund, and on June 2 she pays off the loan. What is the payoff amount? Due date Date received otal payment Interest Principal Balance May 24 $1, June 2 $1, $2.90 $1, $0.00 Procedure Number of days: 7 days in May (31-24 = 7) + 2 days in June = 9 9 Interest: I = PR = $1, % 365 = $2.90 Principal: $1, (previous balance) otal payment: $ $1, = $1, You get a $120,000 mortgage loan for 30 years at 6.75% interest. he lender requires an escrow account. Property taxes are currently $1,958 per year and insurance is currently $785. alculate your total monthly payment (PII). N i PV PM V = = , PM = PV(i) 1 = = $ $120,000 ( ) 1 ( ) 360 ol,.5625%, n = 360: PM = $120, = $ =PM(i, n, PV, V, Mode) =PM(6.75%/12, 30*12, , 0, 0) ($778.32) PI (above) $ I: ($1,958 + $785) PII $1, Practice est 223