Question

13. You can afford a $1,800 per month mortgage payment. You've found a 30-year loan at 5.5% interest.(a) How big of a loan can you afford? $(b) How much total money will you pay the bank? $(c) How much of that money is interest? $

Answer 1

Explanation:

Given

Principal = $1,800

interest rate = 5.5%

Using the below formula to calculate the mortgage

`\begin{gathered} m\text{ = }\frac{p\cdot\text{ r (}1+r)^n}{(1+r)^n\text{ - 1}} \\ \text{Where P = principal, r = interest rate} \\ m\text{ = \$1800} \\ r\text{ = 5.5\% } \\ r\text{ = }(5.5)/(100)\text{ = 0.055} \\ \text{ since it is per month, hence the interest rate is given as} \\ r\text{ = }(0.055)/(12)\text{ = 0.00458} \\ n\text{ = 12 }\cdot\text{ 30} \\ n\text{ = 360} \\ 1800\text{ = }\frac{P\cdot0.00458(1+0.00458)^(360)}{(1+0.00458)^(360)\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458(1.00458)^(360)}{(1.00458)^(360)\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458\cdot\text{ 5.1812}}{5.1812\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot\text{ 0.0237}}{4.1812} \\ \text{Cross multiply} \\ 1800\cdot\text{ 4.1812 = P }\cdot\text{ 0.0237} \\ 7526.16\text{ = P }\cdot\text{ 0.0237} \\ p\text{ = }(7526.16)/(0.0237) \\ P=\text{ \$317, 559. 50} \end{gathered}`

Hence, the loan he can afford is $317, 559. 50

Part B

The total money he will pay to the bank is calculated as follows

Total amount = 1800 * 360

Total amount = $648, 000