Assume you need a $98,000.00 loan for a home. Compute the monthly payment for each option. Assume that the loans are fixed rate and that closing costs are the same in both cases. Round to the nearest penny.

Option 1: a 30 year-loan at an APR of 6.25%

Option 2: a 15 year-loan at an APR of 5.5%

To calculate the monthly payments for each option, we can use the formula for monthly mortgage payments:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (in this case, $98,000),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of payments (loan term in years multiplied by 12).

Let's calculate the monthly payments for each option:

### Option 1: 30-year loan at 6.25% APR
- Loan amount ($P$) = 98,000
- Annual interest rate = 6.25%
- Monthly interest rate ($r$) = $\frac{6.25\%}{12} = 0.0520833\%$
- Loan term = 30 years, so the number of payments ($n$) = 30 × 12 = 360

### Option 2: 15-year loan at 5.5% APR
- Loan amount ($P$) = 98,000
- Annual interest rate = 5.5%
- Monthly interest rate ($r$) = $\frac{5.5\%}{12} = 0.0458333\%$
- Loan term = 15 years, so the number of payments ($n$) = 15 × 12 = 180

I'll calculate the monthly payments for both options.The monthly payments for each option are:

- **Option 1**: 30-year loan at 6.25% APR → $603.40 per month
- **Option 2**: 15-year loan at 5.5% APR → $800.74 per month

Would you like further details on how these calculations were made, or do you have any questions?

Here are 5 related questions for exploration:
1. What is the total interest paid over the life of each loan?
2. How does a 20-year loan compare to the 15- and 30-year options?
3. How much would you save in total payments by choosing the 15-year loan?
4. What if the APR for the 30-year loan was reduced to 5.5%?
5. How would a different loan amount (e.g., $150,000) affect the monthly payments?

**Tip**: Shorter loan terms usually have higher monthly payments but lower total interest paid over time.

Assume you need a $98,000.00 loan for a home. Compute the monthly payment for each option. Assume that the loans are fixed rate and that closing costs are the same in both cases. Round to the nearest penny. Option 1: a 30 year-loan at an APR of 6.25%. Option 2: a 15 year-loan at an APR of 5.5%.

Learn how to compute monthly mortgage payments for a $98,000 home loan. Compare a 30-year loan at 6.25% APR and a 15-year loan at 5.5% APR using loan amortization formulas. Suitable for finance students and those interested in home loan calculations.

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