Question

Seven years ago, Carlos took out a 30-year mortgage for $185,000 at 5.6 percent. He has made all of the monthly payments as agreed. What is his current loan balance

Answer 1

Answer:

Remaining balance of loan after 7 years ( today ) = $ 164,619.6

Explanation:

amount of mortgage = $ 185,000

original term of loan 30 years * 12 = 360 months

interest rate = 5.6 % * 1/12 =0.4666% per month

monthly payment = amount oa mortgage * i /[ 1- (1+i)^-n ]

= $ 185,000 * 0.4666% / [ 1- ( 1 +0.4666%)^-360 ]

= $ 863.21 / [ 1 - 0.187148 ]

= $ 863.21 / 0.812852

= $ 1061.95

after 7 years, that means 84 months, remaining term = 360 months - 84 months = 276 months

remaining balance of loan = amount of loan * ( 1+ i )^n - monthly payment * [ {( 1 + i )^n - 1 } / i ]

remaining balance of loan after 7 years ( 84 months ) = [ $ 185,000 * ( 1+0.4666%)^84 ] - $ 1061.95 * [ {(1+0.4666%)^84 - 1} / 0.4666 ]

= [ $ 185,000 * 1.47850 ] - $ 1061.95 * ( 0.47850 / 0.4666% ]

= $ 273,522.5 - $ 1061.95 * 102.55

= $ 273,522.5 - $ 108,902.9

= $ 164,619.6

remaining balance of loan after 7 years ( today ) = $ 164,619.6