Question

The next four questions are related to your purchase of your first home for $600,000.

You have just purchased the house and have put a 20% down payment, and will borrow the remaining amount.  The 15-year fixed rate loan has an Annual Percentage Rate (APR) of 3.875%.   You will make monthly payments for the life of the loan.

You've made mortgage payments for the first year of the loan. How much have you made in principal payments. Stated differently, by how much did you reduce the loan balance?

Select one:

a. $17,000 to $19,000

b. Less than $15,000

c. $15,000 to $17,000

d. $19,000 to $21,000

e. More than $21,000

Answer 1

Step 1: Find the loan amount.

Loan amount = Purchase price - down payment.
= 600,000 - (20% of 600,000)
= 600,000 - 120000
= $480,000

Step 2: Find Monthly payment. Use present value of annuity formula:

Where,
PVA = Present Value of Annuity
A = Annuity or Payment
i = rate of interest
n = number of years
a = number of payments per year
na = total number of payments

Therefore monthly payment = $3,520.51

Step 3: Find balance of loan after 1 year of payment. That is after 12th payment.

We can use the balance of loan formula, to answer this question.

Where,
PV = Present value / original balance.
here, n = 1

So principal balance after one year of payment is  $455,929.37

Step 4: Step 1 - Step 3

Principal amount at beginning is 480,000 and balance is  455,929.37. Therefore,

Principal paid in one year = 480,000 -  455,929.37
= $24,070.63

So the answer is e. More than $21,000

Easy method: Paste following formula in an excel cell, you will get the answer.

=-CUMPRINC(3.875%/12,15*12,480000,1,12,0)