Question

You have deposited $96,780 into an account that will earn an interest rate of 15% compounded semiannually. How much will you have in the account by the end of 14 years?

Answer 1

Answer:

After 14 years, the compounded value of the invested amount = $733,200.27

Explanation:

What the question is asking us to find is the future value of an amount that is invested over a period of 14 years, compounded at 15% semiannually.

The formula is:

$FV= PV(1 + \frac{i}{n} )^{nt}$

where ;

FV = Future value

PV = present value (principal)

i = nominal interest

n = compounding frequency in a year

t = total number of years.

Note: for investments that are compounded annually, n = 1, because compounding is once in a year, for those compounded semiannually, n=2, because compounding is twice in a year, for compounding done quarterly, n = 4 because there are four quarters in a year and so on.

Putting, the values into the equation above;

$FV=PV(1 + \frac{r}{n}) ^{nt}$

$= 96,780(1 + \frac{0.15}{2} )^{(2*14)} = 96,780 (1 + 0.075)^2^8\\ = 96,780 (7.5759882436) = 733,200.27$

= $733,200 (to the nearest dollar)