Question

A fixed-payment loan has an annual payment of $800 for 15 years. If the interest rate is 7.9%, what is the loan amount (in $)?

Answer 1

Here, the payments will be same every year, so it is an annuity. We need to calculate present value of annuity here. We will use the following formula:

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

where, PVA = Present value of annuity, P is the periodical amount = $800, r is the rate of interest = 7.9% and n is the time period = 15

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

PVA = $800 * (1 - (1 + 7.9%)^-15 / 7.9%)

PVA = $800 * (1 - ( 1+ 0.079)^-15 / 0.079)

PVA = $800 * (1 - ( 1.079)^-15 / 0.079)

PVA = $800 * (1 - 0.31965266513) / 0.079)

PVA = $800 * (0.68034733487 / 0.079)

PVA = $800 * 8.611991580632

PVA = $6889.59

So, loan amount is $6889.59.