Question

Matt plans to start his own business once he graduates from college. He plans to save $2,000 every six months for the next four years. If his savings earn 8% annually (or 4% every six months), determine how μch he will save by the end of the fourth year.

a) $16,000
b) $17,120
c) $18,265.60
d) $19,448.64

Answer 1

Matt will save $19,448.64 by the end of the fourth year.

The corect answer is D.

Step-by-step explanation:

To determine how much Matt will save by the end of the fourth year, we need to calculate the future value of his savings using compound interest. Matt plans to save $2,000 every six months for the next four years. Since his savings earn 4% every six months, or 8% annually, we will use this as the interest rate.

First, we need to convert the interest rate to a semi-annual rate. The formula to convert an annual interest rate to a semi-annual interest rate is: (1 + annual rate)^(1/2) - 1.

Using this formula, we find that the semi-annual interest rate is 2%. Now we can calculate the future value of Matt's savings:

Future Value = $2,000 * ((1 + 0.02)^8 - 1) / 0.02

Calculating this expression gives us a future value of $19,448.64.

The corect answer is D.