Question

You invested $1,350 in an account that pays 3 percent simple interest. How much more could you have earned over a 4-year period if the interest had compounded annually?

$7.81

$7.13

$16.94

$7.07

$7.44

Answer 1

The answer is $7.44

Explanation:

Investment amount is $1,350.

At 3% simple interest the earning would be = P *(1 + r *t)

Where,

P = Principal

r = annual interest rate

t = number of years

Therefore,

Final amount = 1350 * (1 + ((3/100) *4))

                       = 1512

Total interest earned = 1512 – 1350

                                    = 162

The total interest therefore earned at 3% simple interest for 4 years is $162

At 3% interest compounded annually the earning would be = P * (1 +r/n)^nt

Where,

P = Principal

r = annual interest rate

t = number of years

n = number of times interest is applied over period t

Therefore,

Final Amount = 1350 * (1 + 0.03/1) ^ 1 *4

                       = 1519.437

Total interest earned = 1519.437 – 1350

                                    = 169.437

The total interest therefore earned at 3% compounded annually for 4 years is $169.437

Difference in earning = 169.437 – 162

                                    = 7.437

                                    = 7.44

Therefore $7.44 could be earned more if the 3% interest in compounded annually.