Question

You are looking at a one-year loan of $5,000. The interest rate is quoted as 8 percent plus 4 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay 4 points to the lender up front and repay the loan later with 8 percent interest. What rate would you actually be paying here?

Answer 1

Answer -

Following are given in the question:

1. Present value of Loan (PV) = $5,000
2. Time Period (N) = 1 Year
3. Rate = 8% plus 4 points

We need to pay the principal with 8% interest and we need to pay 4% interest upfront.

Hence we need to pay NOW = 0.04 * $5,000 = $200

After 1 year we will pay (FV) = (1 + .08) * $5,000 = $5,400

Now, we have updated PV = $5,000 - $200 = $4,800

We can calculate the rate which we are actually paying by using the below mentioned formula -

FV = PV(1 + R)^N

Where -

PV = $4,800 (calculated above)

FV = $5,400 (calculated above)

N = 1 (given)

On putting these figures in the above formula, we get -

FV = PV(1 + R)^N

$5,400 = $4,800(1 + R)¹

$5,400 / $4,800 =1 + R

($5,400 / $4,800) – 1 = R

R = 0.125, or

R = 12.50%

Hence the rate which we are actually paying here is 12.50%