Question

the house is $360,916 - Broker offered t o 6. 29 total points. You have decided that you will start a savings plan. You will deposit $20 per week into an account that you think will pay 8% per year. al year 52wak 15 years = 15x52 = 780 A. 10 points. How much will you have in 15 years? B. 12 points. Suppose that, with your savings, you will buy a house after 15 years. In addition to your dov payment, you will borrow $400,000. If the interest rate is 3.6% on your 30 year mortgage. What will be yo monthly payment? C. 2 points. Suppose that the down payment is equal to what you will have in your saving account. How much does your home cost? D. 5 points. How much total interest will you have paid once your mortgage is paid off?
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Answer 1

A.

$\begin{align*}\text{Future Value}&= \text{Periodic Payment}\left(\frac{\left(1+\text{Rate Per Period}\right )^\text{No. of years}}{\text{Rate Per Period}} \right )\\&=\left( \$20\times 52\;\text{Weeks}\right )\left(\frac{\left( 1+0.08\right )^1^5}{0.08} \right )\\&=\$41,238.19 \end{align*}$

B.

$\begin{align*}\text{Discounting Factor}&= \left(\frac{\left(1+\text{Rate Per Period}\right )^\text{No. of years}-1}{\text{Rate Per Period}\left(1+\text{Rate Per Period}\right )^\text{No. of years}} \right )\\&=\left(\frac{\left( 1+0.036\right )^3^0-1}{0.036\left( 1+0.036\right )^3^0} \right )\\&=18.163 \\\text{Monthly Payment}&=\frac{\text{Loan Amount }}{\text{Discounting Factor}\times 12 \;\text{Months}}\\&=\frac{\$400,000}{18.163\times12}\\&=\$1,835.23 \end{align*}$

C.

$\begin{align*}\text{Cost of House}&=\text{Loan Amount}+\text{Down Payment}\\&=\$400,000+\$41,238.19\\&=\$441,238.19 \end{align*}$

D.

Loan Amount Interest Paid = No. of Years -- Monthly Payment $400,000 - $1,835.23 30 = $11, 498.10 =