principal balance at the end of 2years?

Question

Hi

would greatly appreciate anyone to go through and show me how to get the answer algebraically. Teacher just confuses me.

 

Shawna recieved a student loan of $30000 at 6%compounded monthly. If she has to repay $400 at the end of every month, what will be her principal balance at the end of 2 years?

 

thanks in advance :)

Answer 1

Let's use this formula: B = A(1+i)ⁿ - (P/i)*([1+i]ⁿ - 1), where B is the balance after n payments, A is the initial amount of the loan, P is the monthly payment amount, and i is the interest rate compounded monthly.

 

1. A = 30000, P = 400, i = .06/12 = .005, and n = 2 years*(12 months/1 year) = 24 payments

2. substitute the values: 30000(1+.005)²⁴ - (400/.005)*([1+.005]²⁴ - 1) ≈ 23642.01

3. therefore, the loan balance after 24 months (i.e. 24 payments) ≈ $23642.01