SOLUTION: Finite mathematics- Beth obtained a student loan of $75,000 to finish her last two years of medical school. She would make no payments until she finished, but the loan would ac

Question 1158933: Finite mathematics-
Beth obtained a student loan of $75,000 to finish her last two years of medical school. She would make no payments until she finished, but the loan would accumulate interest at 2.7% compounded monthly. When she finish school, Beth was to begin monthly payments that would repay the loan in eight years at 2.7% interest.
A) Find the amount of the loan when Beth finished school.
B)Find the monthly payments she should make in order to pay off her debt and eight years.
C) What is the total amount Beth pays over the 10 year period?
D) What is the total amount of interest?

Answer by KMST(5396) (Show Source): You can put this solution on YOUR website!

A) Find the amount of the loan when Beth finished school.
Beth last 2 years of medical school may end 24 months after the loan is obtained or less.
Let's say that Beth will start paying of that loan exactly 24 months after obtaining it.
One month after Beth obtained the loan, the interest added to her debt will be

.
The new balance will be

.
An annual interest of 2.7% compounded monthly multiplies the debt times 1.00225 after a month. 1.1027
At the end of the second months interest on that new balance will be added to the debt, multiplying the balance times again.
After 12 month, with an interest of 2.7% compounded monthly, the new balance would be the loan amount multiplied by ,
as if the interest had been 2.73366% compounded annually.
After 2 years, the balance in the initial loan amount multiplied times (rounded) ,
and Beth's loan balance is (rounded).

B)Find the monthly payments she should make in order to pay off her debt and eight years.
Over the years (120 months) of the loan, not considering the payments, the debt (in $) would have ballooned to
The amount that monthly payments (in $) of would cancel is
,
where each term represents the compounded interest effect of each of the 96 payments, from the last one to the first one.
That long sum is equal to (in $).
To completely cancel her debt including the interest that would have accrued the payment must be such that
--> =

C) What is the total amount Beth pays over the 10 year period?
In $, it should be about (rounded).
The loan authorities will adjust the amount of interest to account for exactly when they received each monthly payment, and the last payment could be adjusted to be more or less than $917.73.

D) What is the total amount of interest?
We could calculate it as
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