Question

At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500, an interest rate of 7.5% compounded monthly, and a duration of ten years. Miranda paid off each loan by making constant monthly payments, starting with when she graduated. All of the loans were subsidized. What is the total lifetime cost for Miranda to pay off her 4 loans? Round each loan's calculation to the nearest cent.

Answer 1

Each year she took a loan of 5500 so after 4 years in college she took out a total of
5500×4 years=22000

Now use the formula of the present value of an annuity ordinary to find the monthly payments to pay off this loan
The formula is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 22000
PMT monthly payment?
R interest rate 0.075
K compounded monthly 12
N time 10 years
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=22,000÷((1−(1+0.075÷12)^(
−12×10))÷(0.075÷12))
=261.1439

The total lifetime cost for Miranda to pay off her 4 loans is the monthly payment times to 12 months times to 10 years
261.1439×12×10=31,337.27

So the answer is 31337.27
Hope it helps!