Suppose you have obtained a 30-year home mortgage in the amount of $248,000 with an APR of 4.25%, compounded monthly. By finding the required monthly mortgage payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years, determine the amount you would save in interest charges by paying off the loan in 20 years.



 $20,725


 $70,636


 $74,161


 $38,848


 None of the above.


To solve this, we'll break the problem down into the following steps:

1. **Determine the monthly mortgage payment for a 30-year term**:
   - Use the mortgage formula for monthly payments:
   
   \[
   M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
   \]
   where:
   - $ M $ is the monthly payment,
   - $ P $ is the loan amount (\$248,000),
   - $ r $ is the monthly interest rate (APR divided by 12),
   - $ n $ is the total number of payments (loan term in months).

   For the 30-year mortgage:
   - $ P = 248,000 $,
   - APR = 4.25%, so $ r = \frac{4.25\%}{12} = 0.0425/12 = 0.00354167 $,
   - The number of months $ n = 30 \times 12 = 360 $.

2. **Determine the monthly mortgage payment for a 20-year term**:
   - Everything is the same except for $ n $, which is now $ 20 \times 12 = 240 $.

3. **Calculate the total payments for each case**:
   - Total payment for 30 years = $ M \times 360 $,
   - Total payment for 20 years = $ M \times 240 $.

4. **Compare the interest paid in both cases**:
   - Interest for 30 years = Total payment for 30 years - Loan amount,
   - Interest for 20 years = Total payment for 20 years - Loan amount,
   - Savings = Interest for 30 years - Interest for 20 years.

Let me calculate the values.### Breakdown of calculations:

- **Monthly payment for a 30-year mortgage**: \$1,220.01
- **Monthly payment for a 20-year mortgage**: \$1,535.70

- **Total interest paid over 30 years**: \$191,203.93
- **Total interest paid over 20 years**: \$120,568.36

- **Savings in interest by paying off the loan in 20 years**: \$70,635.58

Thus, the amount saved in interest charges by paying off the loan in 20 years is approximately **\$70,636**.

The correct answer is **\$70,636**.

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Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would a different APR affect the monthly payment for both 20- and 30-year mortgages?
2. What happens to the total interest paid if the loan amount is increased?
3. How much extra would you need to pay each month to reduce the loan term from 30 years to 25 years?
4. How does a bi-weekly payment system affect the total interest paid?
5. How would the savings change if you made an additional lump-sum payment during the mortgage?

**Tip**: Making extra payments towards the principal early in a mortgage reduces the total interest significantly!

Suppose you have obtained a 30-year home mortgage in the amount of $248,000 with an APR of 4.25%, compounded monthly. By finding the required monthly mortgage payment and also the monthly payment that you would need to make in order to pay off the loan in 20 years, determine the amount you would save in interest charges by paying off the loan in 20 years.

Determine how much you can save in interest charges by opting for a 20-year mortgage instead of a 30-year mortgage on a $248,000 loan with an APR of 4.25%. Learn about monthly payments, interest savings, and the impact of loan duration on overall cost.

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