.We receive a $400,000 mortgage from the Gensinger bank for 100 years. A VP at t

Question

.We receive a $400,000 mortgage from the Gensinger bank for 100 years. A VP at the bank, Robert Littlejohn, tells us to fully amortize the mortgage we need to pay $4,440.820078 monthly. First, we would like to know how much the monthly and yearly mortgage rate the bank charges us. Second, we should find both the nominal and effective annual mortgage rate. Third, we are interested in paying off the total amount in year 30(month360). How much should we give the bank besides the monthly mortgage payment? Fourth, we may have $25,000 to give to the bank additionally to the regular monthly payment in 15 years. How much loan will remain at that point? Fifth, how many more months should we keep paying to eliminate the loan?

Explanation / Answer

1. Monthly and Yearly Mortgage Rate

1.11%

Annual Rate of Interest   13.32%

Using Rate Formula in excel

2. Nominal Annual Mortgage Rate = 13.32% ( 1.11 * 12)

Effective Annual Mortgage Rate = 1 - ( 1 + 0.0111)12 = 14.17%

3. Balance of Loan Amount in Year 30 (Month 360) = $ 399,980.8. So additional amount to be paid = loan balance i.e $ 399,980.8.

4. Loan Balance in year 15 (Month 180) = $ 399,997.72. After payment of additional $ 25,000, loan balance would remain to the tune of $ 374,997.72

5. We have to pay for additional 252 months as per PV of annutiy formula i.e. PV = P ( 1 - ( 1 + r )-n ) / r

1.11%

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