The regular monthly payment M required to repay a loan of P

The regular monthly payment, M, required to repay a loan of P dollars paid n times per year over t years at an annual interest rate r is given by the amortization schedule

a) I just bought a home worth $175 000 at a 4.1 % annual interest rate, and have agreed to pay the bank monthly for 30 years (this is actually true). Calculate my monthly mortgage payments.

b) If I had taken the same balance as a principal at the same 4.1% interest rate as a compound interest loan instead (compounded monthly), and paid the bank a lump sum after 30 years had ended, how much money would I have saved using the amortization schedule?

Solution

Borrowed amount = 175000

Interest rate = 4.1% annual

Period = 30 years = 360 months equal instalments

The EMI works out to be Rs.845.60

Hence total amount repaid = 845.60x360 = 304416

Principal 175000

Interest 129416

Monthly payment 845.60

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b) When interest compounded monthly:

If compounded monthly effective annual rate would be

(1+0.041/12)¹²

⁼ 1.0417793-1 = 4.17793%

In that case, equal monthly instalments would work out to

853.43

Thus extra amount paid = 853.43-843.60 = 9.83 per month

Hence total saving by adopting yearly compounding =9.83 x 360 = 3538.80