Question

Beatrice invests $1,360 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually

Answer 1

Answer:

If the interest was compounded annually, the amount that would have been earned more over the simple interest method is $7.49

Explanation:

A simple interest account pays interest on only the sum deposited at an annual rate for a specified period of time while a compounding interest account adds the interest earned in each period to the principal amount and calculate the interest for the next period on this new amount (Principal + Accumulated Interest).

The formula to calculate interest under simple interest method is,

Interest = Principal * Annual Rate * Time in years

Total Interest earned = 1360 * 3% * 4

Total interest earned = 163.2

The formula to calculate interest under compound interest method is,

Interest = [Principal * (1+i)^t] - Principal

Where,

• i is the interest rate
• t is the number of periods

Interest = 1360 * (1+0.03)^4 - 1360

Interest = 170.6919 rounded off to $170.69

If the interest was compounded annually, the amount that would have been earned more over the simple interest method is,

Extra amount = 170.69 - 163.2

Extra amount = $7.49