Question

Todd opened a savings account and deposited $400.00. The account earns 4% interest, compounded annually. If he wants to use the money to buy a new bicycle in 2 years, how much will he be able to spend on the bike?

A) $416.00
B) $408.16
C) $424.32
D) $432.00
E) $440.96

Answer 1

Todd will have $432.64 after 2 years to spend on a new bicycle due to the compound interest on his initial $400.00 deposit at a 4% annual rate, compounded annually.

Step-by-step explanation:

Calculating Compound Interest

Todd opened a savings account with a $400.00 deposit that earns 4% interest, compounded annually. To determine how much money Todd will have in 2 years to spend on a new bicycle, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Since the interest is compounded annually, n = 1. Therefore, we can calculate the total amount Todd will have after 2 years:

A = 400(1 + 0.04/1)^(1*2) = 400(1 + 0.04)^2 = 400(1.04)^2 = 400 * 1.0816 = $432.64

After 2 years, Todd will have $432.64 to spend on the bike. Thus, the answer is option D) $432.00 if we are rounding to the nearest dollar.