Question

A $200,000 loan amortized over 12 years at an interest rate of 10% per year requires payments of $21,215.85 to completely remove the loan when interest is charged on the unrecovered balance of the principal. If interest is charged on the original principal instead of the unrecovered balance, what is the loan balance after 12 years provided the same $21,215.85 payments are made each year?

Answer 1

Answer:

loan balance after 12 years = $185409.8

Explanation:

Loan principal = $200000

interest = 10% of principal

amount paid yearly  = $21215.85

For 1st year

principal for the first year = $200000

required interest to be paid = 10% of 200000 = $20000

amount paid = $21215.85

Loan Balance after first year = (principal for first year) - (amount paid - 10% of principal ) = $198,784.15

For 2nd year

principal for the 2nd year = Loan balance after first year = $198,784.15

loan balance after 2nd year = 198784.15 - ( 21215.85 - 10% of 198784.15)

= $197568.30

same applies for the different years until the 12th year

using this formula :

Loan Balance after Nth year = [ Loan balance after (n-1) year - ( amount paid - 10% of loan balance after (n-1) year ) ]