5. (Related to Checkpoint 5.2) (Compound interest with non-annual periods) You j

Question

5. (Related to Checkpoint 5.2) (Compound interest with non-annual periods) You just received a bonus of $4,000 a. Calculate the future value of $4,000, given that it will be held in the bank for 9 years and eam an annual interest rate of 5 percent b. Recaicuiale part (a) using a compounding period that is (1) semiannual and (2) bimoninly c. Recalculate parts (a) and (b) using an annual interest rate of 10 percent d. Recalculate part (a) using a time horizon of 18 years at an annual interest rate of 5 percent e What conclusions can you draw when you compare the answers in parts (c) and (d) with the answers in parts (a) and (b)? a. What is the future value of $4,000 in a bank account for 9 years at an annual interest rate of 5 percent? Round to the nearest cent.) b. What is the fulure value of $4,000 in a bank account for 9 years at 5 percent compounded semiannually? Round to the nearest cent.) What is the future value of $4,000 in a bank account for 9 years at 5 percent compounded bimonthly? (Round to the nearest cent.) c. What is the future value of $4,000 in a bank account for 9 years at an annual interest rate of 10 percent? Round to the nearest cent.) What is the future value of $4,000 in a bank account for 9 years at 10 percent compounded semiannually? (Round to the nearest cent.) What is the future value of $4,000 in a bank account for 9 years at 10 percent compounded bimonthly? (Round to the nearest cent) d. What is the future value of $4,000 in a bank account for 18 years at an annual interest rate of 5 percent? (Round to the nearest cent.) e. With respect to the effect of changes in the stated interest rate and holding periods on future sums, which of the following statements is correct? (Select the best choice below.) O A. An increase in the stated interest rate will increase the future value of a given sum. Likewise, O B. An increase in the stated interest rate will decrease the future value of a given sum. Whereas, O C. An increase in the stated interest rate will decrease the future value of a given sum. Likewise O D. An increase in the stated interest rate will increase the future value of a given sum. Whereas, an increase in the length of the holding period will increase the future value of a given sum an increase in the length of the holding period will increase the future value of a given sum an increase in the tength of the holding period will decrease the future value of a given sum. an increase in the length of the holding period will decrease the future value of a given sum.

Explanation / Answer

Part A

Interest Rate = 5%

Time = 9 years

PV = 4,000

FV = 4,000 * (1 + 5%)9

FV = 6,205.31

Part B

Interest Rate = 5%

Semi Annual Rate = 2.5%

Time = 9 years

Semi Annual Periods = 18

PV = 4,000

FV = 4,000 * (1 + 2.5%)18

FV = 6,238.63

Part C

Interest Rate = 5%

bimonthly Rate Rate = 5%/6

Time = 9 years

bimonthy Periods = 9 * 6 = 54

PV = 4,000

FV = 4,000 * (1 + 0.8333333%)54

FV = 6,261.56

Part D

Interest Rate = 10%

Time = 9 years

PV = 4,000

FV = 4,000 * (1 + 10%)9

FV = 9,431.79

Part E

Interest Rate = 10%

Semi Annual Rate = 5%

Time = 9 years

Semi Annual Periods = 18

PV = 4,000

FV = 4,000 * (1 + 5%)18

FV = 9,626.48

Part F

Interest Rate = 10%

bimonthly Rate Rate = 10%/6

Time = 9 years

bimonthy Periods = 9 * 6 = 54

PV = 4,000

FV = 4,000 * (1 + 1.66667%)54

FV = 9,765.70

Part G

Interest Rate = 5%

Time = 18 years

PV = 4,000

FV = 4,000 * (1 + 5%)18

FV = 9,626.48

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