Question

Suppose you would like to save P9000 invested at 8% compounded quarterly for 5 years and 6 months. (Note: Round off your answer to the nearest hundredth) (a) How much would the value of her savings at the end of the term? Answer (b) How much is the interest earned by your savings? Answer

Answer 1

a) 13913

b) 4913.82

Explanation:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

Investment of 9000, so
`P = 9000`

Interest rate of 8%, so
`r = 0.08`

Compounded quarterly, so
`n = 4`

5 years and 6 months, that is, 5 years and half, so
`t = 5.5`

(a) How much would the value of her savings at the end of the term?

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

`A(5.5) = 9000(1 + (0.08)/(4))^(4*5.5) = 13913.82`

(b) How much is the interest earned by your savings?

The amount subtracted by the principal. So

13913.82 - 9000 = 4913.82