Let's break down the calculation into several steps.
1. First, we will calculate the amount of interest that accrued over the 3 years that Boris was in school. This will be calculated using the formula for simple interest, which is:
I = PRT,
where:
I is the interest,
P is the principal amount (the initial amount of money),
R is the rate of interest per period, and
T is the time the money is invested for.
2. Next, we will add this accrued interest to the initial loan amount to find out how much Boris owes when he starts repaying the loan.
3. Finally, we will calculate the monthly payments Boris has to make. This will be calculated using the formula for an amortizing loan, which takes into account both the principal and the interest on the loan. The formula for the monthly payment of an amortizing loan is:
M = P[r(1 + r)^n] / [(1 + r)^n – 1],
where:
M is your monthly payment,
P is the principal loan amount,
r is your monthly interest rate (annual interest rate divided by 12),
n is the number of payments (the number of months you will be paying the loan).
Let's do these calculations.
1. Calculate the accrued interest over the 3 years in school:
I = PRT
I = $15,485 * 6.6/100 * 3
I = $3060.57
2. Calculate the total amount owed at the start of repayment:
Total = Principal + Interest
Total = $15,485 + $3060.57
Total = $18,545.57
3. Calculate the monthly payments:
First, convert the annual interest rate to a monthly rate:
r = 6.6% / 12 / 100 = 0.0055 per month
Then, use the formula for the monthly payment of an amortizing loan:
M = $18,545.57 * [0.0055(1 + 0.0055)^120] / [(1 + 0.0055)^120 – 1]
M = $210.83
So, Boris will have to make monthly payments of approximately $210.83 for 10 years after he graduates.