Question

Isla will deposit $800 in an account that earns 5% simple interest every year. Her sister Aven will deposit $750 in an account that earns 7% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement is true about the balances of the girls’ accounts at the end of 48 months?

Answer 1

To compare the balances of the two accounts, we need to calculate the future value of each account after 48 months.

For Isla's account with simple interest, the interest earned every year is:

$800 x 0.05 = $40

After 48 months (4 years), the interest earned is:

$40 x 4 = $160

So the balance of Isla's account after 48 months is:

$800 + $160 = $960

For Aven's account with compound interest, we can use the formula:

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

where A is the future value, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

For Aven's account, P = $750, r = 0.07, n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:

A = $750(1 + 0.07/1)^(1 x 4) = $1039.14

Therefore, the statement "Aven's account will have a higher balance than Isla's account at the end of 48 months" is true.