Question

Charly is going to deposit 970 in an account that earns 5.8% interest compounded annually. Her sister Robin will deposit 970 in an account that earns 3.2% simple interest each year. They deposit the money on the same day and make no additional deposits or withdrawals from the accounts. Which account will have the most and by how much after 13 years?

Which account will have the most and by how much after 13 years?
A) Robin will have 240.52 more than Charly
B) Charly will have 240.52 more than Robin
C) Robin will have 645.24 more than Charly
D) Charly will have 645.24 more than Robin

Answer 1

Charly's account will have the most after 13 years by $339.69.

Step-by-step explanation:

To determine which account will have the most after 13 years, we need to calculate the compound interest for Charly's account and the simple interest for Robin's account. Charly will deposit $970 in an account that earns 5.8% interest compounded annually. The formula to calculate compound interest is:

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

where A is the total amount, P is the principal amount (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we have:

A = 970(1+0.058/1)^(1*13) = $1,919.49

Robin will deposit $970 in an account that earns 3.2% simple interest each year. The formula to calculate simple interest is:

A = P(1+r*t)

where A is the total amount, P is the principal amount, r is the interest rate, and t is the number of years. In this case, we have:

A = 970(1+0.032*13) = $1,579.80

Therefore, Charly's account will have the most after 13 years, by $339.69. The correct answer is (A) Robin will have $240.52 more than Charly.