a family has a 150000 30 year mortgage at 575 compounded mon

a family has a $150,000, 30 year mortgage at 5.75% compounded monthly. how much is the unpaid blanace after ten years

Solution

principal amount = $150,000

time = 30 years

rate = 5.75% = 0.0575

A = P(1 + r/n)^n*t

n = 12                     // compounded monthly

A = 150000 * (1 + 0.0575/12)^12*30

A = 150000 * (1.00479)³⁶⁰

A = 150000 * 5.5894

A = $ 838410

this is the total amount to be paid after 30 years

therefore amount paid every year = 838410 / 30 = $ 27947

money paid in 10 years = money paid each year * number of years                  (number of years = 10)

                                      = 27947*10

                                      = $ 279470

Unpaid balance = total amount - amount paid in 10 years

                           = 838410 - 279470

                           = $ 558940