Ch04 Time Value Of Money practice questions_w_solution

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1 Chapter 4 The Time Value of Money Practice Questions With Solutions. True / False Questions 1. Compound interest pays interest for each time period on the original investment plus the accumulated interest. True False 2. For a given amount, the lower the discount rate, the less the present value. (should be the higher the present value) True False 3 Converting an annuity to an annuity due decreases the present value. (should increase) True False 4 An effective annual rate must be greater than an annual percentage rate. (not necessary. If just compounded annually once a year, EAR will be the same as APR) True False 5 You should never compare cash flows occurring at different times without first discounting them to a common date. True False 6 An annuity due must have a present value at least as large as an equivalent ordinary annuity. True False Multiple Choice Questions 7 What is the future value of $10,000 on deposit for 5 years at 6% simple interest? A. $7,472.58 B. $10,303.62 C. $13,000.00 D. $13,382.26 Answer: using simple interest FV=10,000+ 5*10,000*6%=13,000 If using compounding interest FV=10,000*(1+6%)^5 8 Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate? A. The interest rate is very high. B. The investment period is very long. C. The compounding is annually. D. This is not possible with positive interest rates. 9 How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually? A. $70.00 B. $80.14 C. $105.62
2 D. $140.00 Answer:1000*(1+0.07)*(1+0.07)*0.07=80.14 10 Assume the total expense for your current year in college equals $20,000. How much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount? A. $952.46 B. $1,600.00 C. $1,728.08 D. $3,973.11 FV=20,000, I/Y=8, N=21, PMT=0, CPT PV= 11 How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually? A. 9.81 years B. 14.27 years C. 22.01 years D. 25.00 years Financial Calculator PV=1,000, FV=-3000, I/Y=8, PMT=0, CPT N=14.27 Excel NPER(0.08,0,1000,-3000)=14.27 12 Given a set future value, which of the following will contribute to a lower present value? A. Higher discount rate B. Fewer time periods C. Less frequent discounting D. Lower discount factor Answer: the relationship between FV and PV is inverse from this equation FV=PV*(1+r)^N when the interest rate is positive. 13 If the future value of an annuity due is $25,000 and $24,000 is the future value of an ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate? A. 1.04% B. 4.17% C. 5.00% D. 8.19%
3 Still remember PV(Annuity)*(1+r)=PV (Annuity Due). R=25000/24000-1=4.17% 14 How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%? A. $3,604.78 B. $3,746.25 C. $4,037.35 D. $4,604.78 Answer: this is to find PV of a 5 year 1000 annuity Financial Calculator: N=5, PMT=1000, I/Y=12, FV=0, CPT PV=3604.78 Excel: =PV(0.12,5,1000,0)=3604.78 15 You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%? A. $9,731.13 B. $10,412.27 C. $10,524.08 D. $11,524.91 Answer: this is to find PV of an unequal cash flows. Financial Calculator: Input Cash flows in CF key CF0=1000, CO1=2000 F01=1 C02=0 F02=1 C03=4000 F03=1 C04=0 F04=1 C05=6000 F05=1 NPV, I/Y=7, CPT NPV=10412.27 Excel: =NPV(0.07,2000,0,4000,0,6000)+1000=10412.27 16 A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What is its present value? A. $33,333.33 B. $37,681.16 C. $38,333.33 D. $65,217.39
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4 Answer: PV= Payment / r= 5000/0.15=33333.33 Note, use the formula directly. 17 A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond? A. $70.00 B. $252.57 C. $629.56 D. $857.43 In this question, pay attention to “compounded” semiannually. A bond is like a loan, with a face value (principle 1000 in this question) to pay at maturity. No interest is paid. Question ask how much an investor should pay for this bond, AKA, the present value of this bond today. N=20 * 2 =40 (seminally compounded) I/Y= 7/2=3.5 FV=1000 PMT=0, CPT PV= Please also try if it is annually compounded how much it will be, and compare with semiannually compounded to see the difference. 18 Your retirement account has a current balance of $50,000. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually? A. 5.02% B. 7.24% C. 9.80% D. 10.07% This question shows, PV=-50,000, PMT=-6000, N=30, FV=1000000, then CPT I/Y=7.24 Be careful of the sign of PV, PMT and FV. 19. Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding? A. $361,526.14 B. $388,017.16 C. $402,766.67
5 D. $414,008.24 Answer: this is to find PV of an annuity that last for 25 years, but monthly compounding. Number of time preriods should be 25*12, and interest rate should use monthly rate 6%/12 Financial Calculator: N=25*12, PMT=2500, I/Y=6/12, FV=0, CPT PV=388017.16 EXCEL: =PV(0.06/12,25*12,2500,0)=388017.16 20 With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today? A. $112,148.50 B. $120,000.00 C. $123,371.44 D. $133,241.15 PV=1500000, N=30, FV=0, I/Y=8, CPT PMT=? If you did not get the same answer shown here, please read the question again to see what you missed.:) 21. $50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment? A. $2,010.60 B. $5,000.00 C. $15,105.74 D. $20,105.74 Payment = $50,000/[1/.1 - 1/.1(1.1)3] Payment = $20,105.74 Principal payment = $20,105.74 - ($50,000 × .1) Principal payment = $15,105.74 Please try to use financial calculator to solve this problem 22 An amortizing loan is one in which: A. the principal remains unchanged with each payment. B. accrued interest is paid regularly. C. the maturity of the loan is variable. D. the principal balance is reduced with each payment. 23 What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years?
6 A. $771.46 B. $775.90 C. $1,028.61 D. $1,034.53 Payment = $75,000/[(1/.01) - 1/.01(1.01)360] Payment = $771.46 Please try to use financial calculator to solve this problem 24. If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate? A. 4.02% B. 10.02% C. 14.50% D. 15.19% APR = [(1.1608).25 - 1] × 4 APR = .1519, or 15.19% Please try to use financial calculator to solve this problem 25. Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding? A. 8.0% with monthly compounding B. 8.5% with semiannual compounding C. The depositor would be indifferent. D. The time period must be known to select the preferred account. EAR = [1 + (.08/12)]12 - 1 = 8.30% EAR = [1 + (.085/2)]2 - 1 = 8.68% The depositor will prefer the option with the higher EAR (effective annual rate).
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