During four years of college, Nolan MacGregor's student loans are $4,600, $3,500, $3,800, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of annual rate 1%, compounded quarterly while Nolan is in school; and an annual rate of 3%, compounded quarterly during a 6-month grace period after graduation. What is the loan balance after the grace period? Assume the freshman year loan earns an annual rate of 1% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. Round your answer to the nearest cent.

Question

During four years of college, Nolan MacGregor's student loans are $4,600, $3,500, $3,800, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of annual rate 1%, compounded quarterly while Nolan is in school; and an annual rate of 3%, compounded quarterly during a 6-month grace period after graduation. What is the loan balance after the grace period? Assume the freshman year loan earns an annual rate of 1% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. Round your answer to the nearest cent. ​

Quizplus · Accepted Answer

First, we need to calculate the total loan balance at the end of Nolan's college years. To do this, we need to calculate the loan balance for each year separately.

For freshman year, the loan balance after 4 years (including interest) is:

$4,600 x (1 + 0.01/4)^(4*4) = $5,102.79

For sophomore year, the loan balance after 3 years (including interest) is:

$3,500 x (1 + 0.01/4)^(4*3) x (1 + 0.03/4)^(2*4) = $4,013.97

For junior year, the loan balance after 2 years (including interest) is:

$3,800 x (1 + 0.01/4)^(4*2) x (1 + 0.03/4)^(2*3) = $4,323.37

For senior year, the loan balance after 1 year (including interest) is:

$5,000 x (1 + 0.01/4)^(4*1) x (1 + 0.03/4)^(2*2) = $5,935.60

Therefore, the total loan balance at the end of college is:

$5,102.79 + $4,013.97 + $4,323.37 + $5,935.60 = $19,376.73

Next, we need to calculate the loan balance after the grace period. The loans will have accrued interest at an annual rate of 3%, compounded quarterly during the 6-month grace period after graduation. Therefore, the loan balance after the grace period is:

$19,376.73 x (1 + 0.03/4)^(4*(1/2)) = $17,537.74

Therefore, the answer is choice C, $17,537.74.

During Four Years of College, Nolan MacGregor's Student Loans Are