The balance of a loan, B, after n monthly payments is given by B = A(1 - r/1200)

Question

The balance of a loan, B, after n monthly payments is given by B = A(1 - r/1200)^n - P/r/1200 [(1 + r/1200)^n - 1] where A is the loan amount, P is the amount of a monthly payment, and r is the yearly interest rate entered in % (e.g., 7.5% entered as 7.5). Consider a 5-year, $20,000 car loan with 6.5% yearly interest that has a monthly payment of $391.32. Calculate the balance of the loan after every 6 months (i.e., at n = 6, 12, 18, 24, ..., 54, 60). Each time calculate the percent of the loan that is already paid. Display the results in a three-column table, where the first column displays the month, and the second and third columns display the corresponding value of B and percentage of the loan that is already paid, respectively.

Explanation / Answer

Solution:

Given is the formula

B= A((1-r/1200)^n)-((P/(r/1200))*(1+(r/1200)^n)-1)

Also

A= $20, 000

r= 6.5%

P= $391.32

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Month B Interest (of loan paid) 6 18300.28 11.7486 12 15900.9294424 20.495 18 13551.2094424 32.2439

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