Question

The Pets and Pals rescue shelter needs to borrow $50,000 in the form of a mortgage to update its kennel facilities. It agrees to pay the full amount and interest at the end of each year, at a 5 percent rate in 10 annual payments. What will its annual payment be? Please round to the dollar.

Answer 1

Here, the payments will be same every year, so it is an annuity. The present value of annuity is $50000. For calculating the annual payments, we will use the following formula:

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

where, PVA = Present value of annuity = $50000, P is the periodical amount, r is the rate of interest = 5%, and n is the time period = 10

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

$50000 = P * (1 - (1 + 5%)^-10 / 5%)

$50000 = P * (1 - ( 1+ 0.15)^-10 / 0.05)

$50000 = P * (1 - ( 1.05)^-10 / 0.05)

$50000 = P * (1 - 0.61391325354) / 0.05)

$50000 = P * (0.38608674646 / 0.05)

$50000 = P * 7.7217349292

P = $50000 / 7.7217349292

P = $6475.23

So, annual payments will be $6475.23