Question

19. Use a financial calculator or computer software program to answer the following questions. a. What would be the future value (FV) of $19,378 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and interest on the investment is compounded semiannually? b. How would your answer for (a) change if quarterly compounding were used?

Answer 1

Answer : (a)

Calculation of Future value.for which interest on investment is compounded semiannually :

Formula for Future value is

A = P(1+r/n)^nt

Where

A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years

so by using above formula

Amount fr future value = $19378 (1+0.18/2)^2*8

= 19378 (1+0.09)¹⁶

= 19378 (1.09)¹⁶

=19378(3.97)

=$76930.66
Therefore Future value of $19378 invested for 8 years compounded semiannually with 18% interest is $76930.66

Answer : (b)

Calculation of Future value for which interest on investment is compounded quarterly  :

By using above formula

Amount for future value = $19378 (1+0.18/4)4*8

= 19378 (1+0.045)32

= 19378 (1.045)³²

=19378(4.089)

=$79236.64
Therefore Future value of $19378 invested for 8 years compounded quarterly with 18% interest is $79236.64