Question

(Compound interest with? non-annual periods?) You just received a bonus of ?$4,000.

a. Calculate the future value of $1,000, given that it will be held in the bank for 8 years and earn an annual interest rate of 7 percent.

b.Recalculate part (a) using a compounding period that is (1) semiannual and? (2) bimonthly.

c.Recalculate parts (a) and (b) using an annual interest rate of 14 percent.

d.Recalculate part (a) using a time horizon of 16 years at an annual interest rate of 7 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 8 years at an annual interest rate of 7 ?percent $________ ?(Round to the nearest? cent.)

b.What is the future value of $4,000 in a bank account for 8 years at 7 percent compounded? semiannually $________ (Round to the nearest? cent.)

What is the future value of $4,000 in a bank account for 8 years at 7 percent compounded? bimonthly $_________ ?(Round to the nearest? cent.)

c.What is the future value of $4,000 in a bank account for 8 years at an annual interest rate of 7 percent $_________?(Round to the nearest? cent.)

What is the future value of $4,000 in a bank account for 8 years at 7 percent compounded? semiannually $________?(Round to the nearest? cent.)

What is the future value of $4,000 in a bank account for 8 years at 7 percent compounded? bimonthly $_________?(Round to the nearest? cent.)

d.What is the future value of $4,000 in a bank account for 16 years at an annual interest rate of 7 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.)

A.

An increase in the stated interest rate will increase the future value of a given sum. ? Likewise, an increase in the length of the holding period will increase the future value of a given sum.

B.

An increase in the stated interest rate will decrease the future value of a given sum. ? Likewise, an increase in the length of the holding period will decrease the future value of a given sum.

C.

An increase in the stated interest rate will decrease 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.

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 decrease the future value of a given sum.

Answer 1

This question requires application of basic time value of money function: FV = PV * (1 + r)ⁿ

a) PV = $4000, n = 8 years, r = 7% (annual compounding)

FV = 4000 * (1 + 7%)⁸

FV = $6,872.74

b) PV = $4000, n = 8 years, r = 7% (semi-annual compounding)

FV = 4000 * (1 + 3.5%)¹⁶

FV = $6,935.94

bimonthly - can be once in two months or twice in one month, calculating both - use the appropriate one please.

PV = $4000, n = 8 years, r = 7% (bimonthly compounding - once in two months)

FV = 4000 * (1 + 7%/6)⁴⁸

FV = $6,980.03

PV = $4000, n = 8 years, r = 7% (bimonthly compounding - twice in 1 month)

FV = 4000 * (1 + 7%/24)¹⁹²

FV = $6,996.99

c) Annual Rate = 14%

Annual Compounding (Part a)

FV = 4000 * (1 + 14%)⁸

FV = $11,410.35

Semi- Annual Compounding (Part b.1)

FV = 4000 * (1 + 7%)¹⁶

FV = $11,808.65

Bimonthly compounding (Part b,2)

Once in two months:

FV = 4000 * (1 + 14%/6)⁴⁸

FV = $12,102.69

Twice in a month:

FV = 4000 * (1 + 14%/24)¹⁹²

FV = $12,219.59

d) FV = 4000 * (1 + 7%)¹⁶

FV = 11,808.65

e) Statement A is correct. FV is directly proportional to rate of interest or number of holding periods. Higher the rate of interest or the number of holding periods, higher would the FV be.