Question

Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest. A. how much does she have in her account at the end of 3 years? B. at what annual simple interest rate did the account grow? c. how many more dollars would she have in her account if the interest rate were 1% greater?

Answer 1

A) The amount at the end of 3 years is $4960

B) Rate of interest is 8 % per annum

C) Yvonne would have had $120 more should the rate were 1% greater

Solution:

Given that,

Yvonne put $4,000 in a savings account

At the end of 3 years, the account had earned $960 in simple interest

A. how much does she have in her account at the end of 3 years

Amount = principal + simple interest earned

Amount = 4000 + 960

Amount = 4960

Thus the amount at the end of 3 years is $4960

B. at what annual simple interest rate did the account grow?

Rate of interest = ?

Simple interest is given by formula:

`Simple\ interest = (p * n * r)/(100)`

Where,

p is the principal

n is the number of years

r is the rate of interest

`960 = (4000 * 3 * r)/(100)\\\\960 = 120r\\\\r = (960)/(120)\\\\r = 8`

Thus rate of interest is 8 % per annum

c. how many more dollars would she have in her account if the interest rate were 1% greater

If the rate was 1% more, R = 8 + 1 = 9% per annum

First find the simple interest for 9 % per annum

`Simple\ interest = (4000 * 3 * 9)/(100)\\\\Simple\ interest = 40 * 3 * 9\\\\Simple\ interest = 1080`

Thus,

amount = simple interest + principal

amount = 1080 + 4000 = 5080

Therefore,

Amount more = $5080 - $4960 = $120

She would have had $120 more should the rate were 1% greater.