You can afford a \( \$ 800 \) per month mortgage payment. You've found a 30 year loan at \( 8 \% \) interest. a) How big of a loan can you afford? Round your answer to the nearest dollar. b) How much total money will you pay the loan company? Round your answer to the nearest dollar. c) How much of that money is interest? Round your answer to the nearest dollar. Question Help: Dost to forum Suhmit Ousction

We start with the standard formula for the monthly payment on a fixed‐rate mortgage:   Payment = P · [r(1 + r)ⁿ] / [(1 + r)ⁿ – 1], where   P = principal (the amount of the loan),   r = monthly interest rate, and   n = number of monthly payments. In this problem:   Monthly Payment = $800,   Annual interest rate = 8%, so the monthly interest rate is    r = 0.08/12 ≈ 0.00666667,   n = 30 years × 12 months/year = 360. It is often simpler to solve for the loan principal by rearranging the formula. Solving for P we have   P = Payment · { [ (1 + r)ⁿ – 1 ] / [ r(1 + r)ⁿ ] }. An equivalent (and often used) formula is   P = Payment · [1 – (1 + r)^(–n)] / r. We now plug in the numbers. Step 1. Compute (1 + r)ⁿ:   (1 + 0.00666667)³⁶⁰. A quick way to compute this is by using logarithms:   ln(1.00666667) ≈ 0.00662252,   so ln[(1.00666667)³⁶⁰] ≈ 360 × 0.00662252 ≈ 2.38411,   and (1.00666667)³⁶⁰ ≈ e^(2.38411) ≈ 10.846. Step 2. Now compute P using the alternate formula:   P = 800 · [1 – (1/10.846)] / 0.00666667. Find (1 + r)^(–n):   (1 + r)^(–n) = 1/10.846 ≈ 0.09219. Then:   1 – (1 + r)^(–n) = 1 – 0.09219 = 0.90781. So the principal is:   P ≈ 800 · 0.90781 / 0.00666667    = 800 × (0.90781 ÷ 0.00666667). Calculate the division:   0.90781 ÷ 0.00666667 ≈ 136.1715. Then:   P ≈ 800 × 136.1715 ≈ 108,937. Thus, (a) the maximum loan amount you can afford is about $108,937. Step 3. To find (b) the total amount paid over the life of the loan, multiply the monthly payment by the number of payments:   Total paid = 800 × 360 = 288,000 dollars. Step 4. To find (c) the total interest paid, subtract the principal from the total amount paid:   Interest = 288,000 – 108,937 = 179,063 dollars. Rounded to the nearest dollar, our answers are: a) Loan amount: $108,937 b) Total paid over 30 years: $288,000 c) Total interest paid: $179,063