## Related questions with answers

Use the following amortization formula: $P = \frac { r \cdot M } { 1 - \left( 1 + \frac { r } { n } \right) ^ { - n t } } \div n$ where P = the payment, r = the annual interest rate, M = the mortgage amount, t = the number of years, and n = the number of payments per year. What is the monthly payment on a mortgage of $120,000 with a 6% interest rate for 20 years? How much interest will be paid over 20 years?

Solution

Verified$\begin{align*} P&=\frac{r \cdot M}{1-\left(1+\frac{r}{n}\right)^{-nt}}\div n && \text{Use the following amortization formula.} \\ &=\frac{0.06 \cdot 120,000}{1-\left(1+\frac{0.06}{12}\right)^{-12 \cdot 20}}\div 12 && \text{Use the given values.} \\ &=\frac{7200}{1-\left(1+0.005\right)^{-240}}\div 12 && \text{Simplify.} \\ &=\frac{7200}{1-0.3} \div 12 && \text{Use a calculator.} \\ &=\color{#c34632}{\$857.14} \end{align*}$

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