Question

The Begays finance $200,000 for a 30-year home mortgage at an annual rate of 5% compounded monthly.

1. Find the monthly payment needed to amortize this loan in 30 years

2. Assume that the Begays make the payment found in part (a) every month for 30 years, find the total interest they

   will pay.

3. Suppose the Begays pay an extra 15% every month ( using Q=d+dr = d + 15%d = (1+ 0.15)d = 1.15d).

   Find the time needed to amortize the $200,000 loan.

4. About how much total interest they will Begays pay if they pay Q every month?

5. About how much will the Begays save on interest if they pay Q rather than d every month?   Formula: t = ln(nQ) - ln (nQ - Pr) / n ln (1+ (r/n))

Answer 1

Loan amount L=200000

Number of payments N=30*12=360

annual rate =5%

Monthly rate r=5%/12=0.417%

Monthly payment d=L*r/(1-(1+r)^-N) =200000*0.417%/(1-(1+0.417%)^-360) =$1073.64

Total Interest pay =N*d-L=360*1073.64-200000=$186511.57

Q=1.15*d =1.15*1073.64=1234.69

Let t be the number of months

L=Q*(1-(1+r)^-t)/r

200000=1234.69*(1-(1+0.417%)^-t)/0.417%

(1+0.417%)^-t=0.325

-t*ln(1+0.417%)=ln(0.325)

t=270.25 Months = 22.52 Years (8 Years)

Tota interest paid = t*Q-L=270.25*1234.69-200000=$133681.71

Saving on interest =186511.57-133681.71=$52829.86