A woman buys an apartment house for $1,250,000 by making a down payment of $325,000 and amortizing the rest of the debt with semiannual payments over the next 11 years. The annual interest rate on the debt is 8%, compounded semiannually. Find the size of each payment. Round your answer to the nearest cent.

Question

A woman buys an apartment house for $1,250,000 by making a down payment of $325,000 and amortizing the rest of the debt with semiannual payments over the next 11 years. The annual interest rate on the debt is 8%, compounded semiannually. Find the size of each payment. Round your answer to the nearest cent. ​

Quizplus · Accepted Answer

The size of each payment can be found using the formula for the payment on an amortizing loan, which is $P = \frac{P_r \times \frac{r}{n}}{1 - (1 + \frac{r}{n})^{-n \times t}}$, where $P_r$ is the principal amount (the initial loan amount), $r$ is the annual interest rate, $n$ is the number of payments per year, and $t$ is the time in years. Here, $P_r = 1,250,000 - 325,000 = 925,000$, $r = 0.08$, $n = 2$ (since payments are semiannual), and $t = 11$. Plugging these values into the formula gives the size of each payment, which is approximately $64,008.90.

A Woman Buys an Apartment House for $1,250,000 by Making