You can afford a $$ \$ 1000 $$ per month mortgage payment. You've found a 30 year loan at $$ 7 \% $$ interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? $$ \$ $$ c) How much of that money is interest? $$ \$ $$ Check Answer

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**a) Calculating the Loan Principal**

Let  
- $$ P = \$1000 $$ be the monthly payment,  
- Annual interest rate $$ = 7\% $$ so the monthly interest rate is  
  $$
  r = \frac{0.07}{12},
  $$
- The number of monthly payments for 30 years is  
  $$
  n = 30 \times 12 = 360.
  $$

For a fixed-rate mortgage the monthly payment is given by
$$
P = L \cdot \frac{r(1+r)^n}{(1+r)^n - 1},
$$
where $$ L $$ is the loan principal. We solve this equation for $$ L $$:
$$
L = P \cdot \frac{(1+r)^n - 1}{r(1+r)^n}.
$$

Plug in the values:
$$
L = 1000 \cdot \frac{\left(1+\frac{0.07}{12}\right)^{360} - 1}{\frac{0.07}{12}\left(1+\frac{0.07}{12}\right)^{360}}.
$$

Calculating step by step:

1. Compute the monthly interest rate:
   $$
   r = \frac{0.07}{12} \approx 0.0058333.
   $$

2. Compute $$\left(1+r\right)^{360}$$:
   $$
   \left(1+0.0058333\right)^{360} \approx 8.108.
   $$
   
3. Compute the numerator:
   $$
   (1+r)^{360} - 1 \approx 8.108 - 1 = 7.108.
   $$

4. Compute the denominator:
   $$
   r(1+r)^{360} \approx 0.0058333 \times 8.108 \approx 0.04727.
   $$

5. Finally, compute $$ L $$:
   $$
   L \approx 1000 \times \frac{7.108}{0.04727} \approx 1000 \times 150.34 \approx \$150,\!340.
   $$

Thus, the loan you can afford is approximately $$\$150,\!340$$.

---

**b) Total Amount Paid Over the Life of the Loan**

The total amount paid is simply the monthly payment multiplied by the number of payments:
$$
\text{Total paid} = P \times n = 1000 \times 360 = \$360,\!000.
$$

---

**c) Total Interest Paid**

The total interest paid is the difference between the total amount paid and the principal:
$$
\text{Interest paid} = \$360,\!000 - \$150,\!340 \approx \$209,\!660.
$$

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**Final Answers:**

a) The loan principal is approximately $$\$150,\!340$$.  
b) The total amount paid over 30 years is $$\$360,\!000$$.  
c) The total interest paid is approximately $$\$209,\!660$$.
a) You can afford a loan of approximately \$150,340. b) Over 30 years, you'll pay a total of \$360,000. c) Of that, about \$209,660 will be interest.

You can afford a per month mortgage payment. You’ve found a 30 year loan at
interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
Check Answer

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You can afford a per month mortgage payment. You’ve found a 30 year loan at interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest? Check Answer