Question

phil has been accepted into a 2 year radiology technician program at a career school. he has been awarded $9000 unsubsidized 10 year federal loan at 4.29%. he knows he has the option of beginning repayment of the loan in 2.5 years. he also knows that during this nonpayment time, interest will accrue at 4.29%. if phil decides to make no payments during the 2.5 years, the interest will be capitalized at the end of that period. what will the new principal be when he begins making loan payments?

Answer 1

Phil's new loan principal after 2.5 years of compounded interest at a rate of 4.29% on his original $9,000 loan will be approximately $9,999.35.

Step-by-step explanation:

Phil has been accepted into a 2-year radiology technician program and has been awarded a $9,000 unsubsidized federal loan at a 4.29% interest rate. During the 2.5 years of nonpayment time, interest will accrue and then be capitalized into the principal. To calculate the new principal when Phil begins making loan payments, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($9,000), r is the annual interest rate (4.29%), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years (2.5 years in this case).

Since the interest is capitalized at the end of the nonpayment period, we can consider it to be compounded once at that point, so n = 1. Therefore, we calculate the new principal as:

A = $9,000(1 + 0.0429/1)^(1*2.5) = $9,000(1 + 0.0429)^2.5 = $9,000(1.0429)^2.5 = $9,000 * 1.11115 = $9,999.35

Thus, the new principal amount when Phil begins making loan payments will be approximately $9,999.35.