Question

On june 1, you borrowed $295,000 to buy a house. the mortgage rate is 4.25 percent. the loan is to be repaid in equal monthly payments over 15 years. all taxes and insurance premiums are to be paid separately. the first payment is due on july 1. how much of the first payment applies to the principal balance?

Answer 1

Answer: The amount applied to the principal balance is $1174.43.

We first calculate the Equated Monthly Instalment (EMI) of the loan by using the following formula:

`\mathbf{PV = EMI * \left [(1-(1+r)^(-n))/(r) \right]}`

where

r = Interest rate per period ; n = number of periods

`r = (0.0425)/(12)`

`n = 15 * 12 = 180`

Substituting these in the formula above we get,

`\mathbf{295000 = EMI * \left [(1-(1+(0.0425)/(12))^(-180))/((0.0425)/(12))\right]}`

Solving we get,

`\mathbf{295000 = EMI * 132.9295092}`

`\mathbf{EMI = (295000)/(132.9295092)}`

`\mathbf{EMI = 2219.221313}`

Once we get the EMI, we calculate the amount that applies to the principal balance as follows:

Interest is calculated on the outstanding balance of each month. In the first month, the entire principal in outstanding. Hence we calculate interest on $295,000.

`\mathbf{Interest = 295000 * 0.003541667 = 1044.791667}`

`\mathbf{Amount applied to principal = EMI - Interest in dollars}`

`\mathbf{Amount applied to principal = 2219.221313 - 1044.791667 = 1174.429646}`