The initial monthly payment is established on the assumption that everything stays the same.
The major problem here is the fact that the interest period of compounding is different from the interest period of the payments.
That is, the interest rate is compounded semi-annually, but the payments are monthly.
We have to convert 12% p.a. compounded semi-annually to a monthly rate.
let the monthly rate be i
(1+i)^12 = (1.06)^2
(1+i)^6 = 1.06
take 6th root of both sides
1+i = 1.06^(1/6) = 1.009758794
i = .009758794 ----> I put that in my calucaltor memory
so i = .00975...
n = 12(25) = 300 , and
1000000 = paym(1 - 1.00975..^-300)/.00975...
paym = 10,318.995 or 10,319.00
At the end of 5 years, once you know what the new rate is, you would find the outstanding balance and repeat the above calculation, with n = 240
A bank is willing to give you a Rs1,000,000 home mortgage at 12% interest, compounded semiannually. The loan will be amortised over 25 years, but the interest rate is fixed for only the first 5 years. What is the monthly mortgage payment for the first five years?
Rs 1000,000 = A x (1- 1/¨€((1+0.12)6x25@------------------))
0.12
RS 1000,000 = A x 8.333332992
A = 1000,000/ 8.333332992
A = 120,000.0049
Monthly = 120,000.0049/12
Answer = Rs 10,000.00041
Nearest figure = Rs 10,000
1 answer
1 answer