Consider a loan with a principal 169 60000 annual interest

Consider a loan with a principal - $169, 600.00. annual interest rate - 7.20%, with a monthly payment of $1151.22, and the time = 30 years Determine the remaining balance of the loan after 120 payments are completed.

Solution

For yearly interest rate of 7.2% monthly interest rate = 7.2% / 12 = 0.6%
Initial loan was of 169,600 $ for 30 years with 7.2% annual interest rate and monthly payment of 1151.22
After 120 payments; 10 years would have elapsed; so remaing 20 years of monthly payment of 1151.22 would be left;
Thus the loan amount after 120 payments are completed would be the same as the present value of monthly payment of 1151.22$ for a period of 20 years (240 monthly instalments) = 1151.22 + (1151.22) / (1.006) ¹ + 1151.22/ (1.006)² + ... 1151.22 / (1.006) ²³⁹ = 1,46,215

= 1151.22 ( 1- (1+r) ^-n ) /( r ) = 1151.22 ( 1-0.23794 ) / 0.006 = 1151.22* 127.008 = 146,214.64
Thus the remainging balance after 120 payments are completed is = 146,214.64 ~= 146,215