Present value

A bank loans a family $90,000 at a 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over 15 years. How much should the monthly payment be in order to pay off the debt in 15 years?

Correct answer:

PMT =  688.494

Step-by-step explanation:

$$\begin{gathered} a=90000 \\ p=4.5\%=\frac{4.5}{100}=0.045 \\ t=15 \\ m=12 \\ n=t\cdot m=15\cdot 12=180 \\ r=1+p/m=1+\frac{9}{200}/12=\frac{803}{800}=1\frac{3}{800}\doteq 1.0038 \\ b=1-r^{-n}=1-1.0038^{-180}\doteq 0.4902 \\ PMT=\frac{(r-1)\cdot a}{b}=\frac{(1.0038-1)\cdot 90000}{0.4902}=688.494 \end{gathered}$$

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