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

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