Question

A fully amortizing mortgage loan is made for $90,000 for 15 years. The interest rate is 6 percent per year compounding monthly. Payments are to be made monthly. What is the principal payment in the first monthly payment?

Answer 1

First we will calculate the monthly payments as per below:

Here, the payments will be same every month, so it is an annuity. We will use the present value of annuity formula fo calculating the monthly payments as below:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity = $90000, P is the periodical amount, r is the rate of interest = 6% compounded monthly, so monthly rate = 6% / 12 = 0.5% and n is the time period = 15 * 12 = 180 months

Now, putting these values in the above formula, we get,

$90000 = P * (1 - (1 + 0.5%)-180 / 0.5%)

$90000 = P * (1 - ( 1+ 0.005)-180 / 0.005)

$90000 = P * (1 - ( 1.005)-180 / 0.005)

$90000 = P * (1 - 0.40748242666) / 0.005)

$90000 = P * (0.59251757333 / 0.005)

$90000 = P * 118.503514668

P = $90000 / 118.503514668

P = $759.47

So, monthly payments ar for $759.47

Next, we will calculate the interest in the first monthly payment as per below:

Interest = Principal * Rate of interest * 1 / 12

Interest = $90000 * 6% * 1 / 12 = $450

Now,

In the first monthly payment of $759.47, principal is:

Principal = Monthly payment - Interest

Principal = $759.47 - $450 = $309.47