Question

(Compound interest with non-annual periods) You just received a bonus of $3,000. a.  Calculate the future value of $3,000, given that it will be held in the bank for 5 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 10 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? 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 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. 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 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.

Answer 1

a]

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (7%/1))1*5

future value = $4,207.66

b]

(1)

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (7%/2))2*5

future value = $4,231.80

(2)

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (7%/6))6*5

future value = $4,248.59

c]

Part (a)

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (14%/1))14

future value = $18,784.05

Part (b)

(1)

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (14%/2))2*14

future value = $19,946.52

(2)

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (14%/6))6*14

future value = $20,823.77

d]

future value = present value * (1 + (r/n))n*y

where r = annual interest rate

n = number of compounding periods per year

y = number of years

future value = $3,000 * (1 + (7%/1))1*10

future value = $5,901.45

e]

A is the correct option.

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.