show work, please do not use financial calculator as basis for proof

8. [10] The Smiths buy a home and take out a $160000 mortgage on which the interest rate is allowed to float freely. At the time the mortgage is issued, interest rates are j2 = 6% and the Smiths choose a 25-year amortization schedule. Six months into the mortgage, interest rates rise to j2 = 8%. Three years into the mortgage (after 36 payments) interest rates drop to j2 = 7%, and four years into the mortgage interest rates drop to 12 = 51%. Determine the outstanding balance of the mortgage after 5 years. Note that the interest rate during the remaining 20 years is not necessarily fixed. The monthly payment is set at issue and does not change). 8. [10] The Smiths buy a home and take out a $160000 mortgage on which the interest rate is allowed to float freely. At the time the mortgage is issued, interest rates are j2 = 6% and the Smiths choose a 25-year amortization schedule. Six months into the mortgage, interest rates rise to j2 = 8%. Three years into the mortgage (after 36 payments) interest rates drop to j2 = 7%, and four years into the mortgage interest rates drop to 12 = 51%. Determine the outstanding balance of the mortgage after 5 years. Note that the interest rate during the remaining 20 years is not necessarily fixed. The monthly payment is set at issue and does not change)