Question

Richard is investing money for retirement. He has two different account options available:

Account X pays 2.8% simple annual interest.
Account Y pays 2.8% interest compounded annually.
Richard will deposit $1,200 into the account each year for several years and will make no withdrawals. Which statement is true?

A. Account X and Account Y will have the same balance when Richard retires, because both accounts earn the same interest rate.
B. Account Y will have a larger balance when Richard retires, because an account earning interest compounded annually will earn more money in interest than an account earning simple annual interest when the rates are the same.
C. Account X will have a larger balance when Richard retires, because an account earning simple annual interest will earn more money in interest than an account earning interest compounded annually when the rates are the same.

Answer 1

Regarding the statement about Richard's investment options for retirement, the true statement is B. Account Y will have a larger balance when Richard retires, because an account earning interest compounded annually will earn more money in interest than an account earning simple annual interest when the rates are the same.

Step-by-step explanation:

To determine which account will have a larger balance when Richard retires, we need to compare the effects of simple interest and compound interest over time.

Account X: With simple interest, the interest is calculated only on the initial deposit each year. So after each year, Richard's balance would increase by 2.8% of $1,200.

Account Y: With compound interest, the interest is calculated on both the initial deposit and the accumulated interest from previous years. So after each year, Richard's balance would increase by 2.8% of the current balance including the interest.

As time goes on, compound interest has a compounding effect and will result in a larger total balance compared to simple interest. Therefore, Statement B is true. Account Y will have a larger balance when Richard retires, because an account earning interest compounded annually will earn more money in interest than an account earning simple annual interest when the rates are the same.