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
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
To calculate the monthly mortgage payment for the first five years of a Rs1,000,000 home mortgage at a 12% interest rate, compounded semiannually with a 25-year amortization period, you can use the following formula:
Monthly Payment = Loan Amount / (Number of Payments)
First, calculate the number of payments for the first five years. Since interest is compounded semiannually, there will be 6 payments per year for 5 years, giving us a total of 30 payments.
Next, substitute the values into the formula:
Monthly Payment = Rs1,000,000 / 30
Calculating this, we get:
Monthly Payment = Rs33,333.33
However, this calculation gives us the monthly payment for the entire 25-year amortization period. To find the monthly mortgage payment for only the first five years, we need to further adjust the monthly payment.
Since the interest rate is fixed for the first 5 years, we can calculate the present value of the remaining mortgage balance at the end of the 5-year fixed-rate period. Let's assume the remaining mortgage balance is B.
B = Rs1,000,000 x (1 + 0.12/2)^(2x20)
Calculating this, we get:
B = Rs1,000,000 x 3.68148624569
B = Rs3,681,486.25
Now we need to calculate the monthly payment for this remaining mortgage balance B, which will be amortized over the remaining 20 years of the 25-year loan.
Monthly Payment for remaining balance = B / (Number of Payments)
Number of Payments = 20 x 12 = 240
Monthly Payment for remaining balance = Rs3,681,486.25 / 240
Calculating this, we get:
Monthly Payment for remaining balance = Rs15,339.11
Finally, to find the monthly mortgage payment for the first five years, we add the initial monthly payment to the monthly payment for the remaining balance:
Monthly Mortgage Payment for first five years = Rs33,333.33 + Rs15,339.11
Calculating this, we get:
Monthly Mortgage Payment for first five years = Rs48,672.44
Nearest figure: Rs48,672