Question

Manny took our a 30-year mortgage for $60,000 at 7.5%. How much will he pay over one year?

Answer 1

We have a mortgage of 30 years, with a principal of $60,000 at an interest rate of 7.5%.

We can calculate the annual payments with the annuity formula, with PV = 60000, r = 0.075 and n = 30:

`\begin{gathered} PV=A\cdot(1-(1+r)^(-n))/(r) \\ 60000=A\cdot(1-(1.075)^(-30))/(0.075) \\ 60000\approx A\cdot(1-0.114221)/(0.075) \\ 60000\approx A\cdot(0.88578)/(0.075) \\ 60000\approx A\cdot11.81 \\ A\approx(60000)/(11.81) \\ A\approx5080.27 \end{gathered}`

Answer: he wil be paying $5080.27 each year (assuming yearly payments).