Question

A bank loan requires you to pay $20,000 at the end of each of the next 8 years. The interest rate is 3%. What is the present value of these payments? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Here, the payments will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

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

where, PVA = Present value of annuity, P is the periodical amount = $20000, r is the rate of interest = 3% and n is the time period = 8

Present value of payments = Present value of annuity of $20000 at 3% for 8 years

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

PVA = $20000 * (1 - (1 + 3%)-8 / 3%)

PVA = $20000 * (1 - ( 1+ 0.03)-8 / 0.03)

PVA = $20000 * (1 - ( 1.03)-8 / 0.03)

PVA = $20000 * (1 - 0.78940923431) / 0.03)

PVA = $20000 * (0.21059076569 / 0.03)

PVA = $20000 * 7.019692189666

PVA = $140393.84

So, present value of payments = $140393.84