Question

Taylor and Dakota took out a 30 year mortgage for $135,000 at the APR of 10.1%, compounded monthly. After they had made 13 years of the payments (156 payments) they decide to refinance the remaining loan balance for 20 years at the APR of 5.9%, compounded monthly. What will be the balance on their loan 8 years after the refinance?

Answer 1

Solution: We can calculate sum of the amount usingfollowing formula,

A = P [ 1 + r / t*100 ]^{n *t}

Where A = sum of money after given period n

P = Principal amount (Loan amount)

r = rate of interest per year

n = Number of years

t = 12 (For monthly interest rate)

We have P = $135000 r = 10.1 % per year so we will convert it to monthly interest rate = ( 10.1/12) %

So For t = 30 months we have,

A = 13500 [ 1 + 10.1 / 12*100 ]^{12 *30}

A = $2758920.13989

After 13 years Sum is,

A' = 13500 [ 1 + 10.1 / 12*100 ]^{12 *13}

A' = $499086.80912

Due amount = A - A' = 2758920.13989 - 499086.80912 = $2259833.33077

Now APR rate = 5.9% (Per Year)

So for amount $ 2259833.33077 and   n = 20 years the sum will be,

A" = 2259833.33077 [ 1 + 5.9 / 12*100 ]^{12 *20}

A" = $7333109.95209

After 8 years amount is,

B = 2259833.33077 [ 1 + 5.9 / 12*100 ]^{12 *8}

B = $3618771.19432

So balance after refinance = 7333109.95209 -  3618771.19432

= $ 3714338.75777