In terms of paying less in​ interest, which is more economical for a 

​$80 comma 00080,000 

​mortgage: a​ 30-year fixed-rate at 

77​% 

or a​ 15-year fixed-rate at 

6.56.5​%? 

How much is saved in​ interest? Use the following formula to determine the regular payment amount.

PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFractionPMT=Prn1−1+rn−nt

Question content area bottom

Part 1

Select the correct choice below and fill in the answer box within your choice.

​(Do not round until the final answer. Then round to the nearest thousand​ dollars.)

A.

The​ 15-year 

6.56.5​% 

loan is more economical. The buyer will save approximately 

​$66,00066,000 

in interest.  

Your answer is not correct.

B.

The​ 30-year 

77​% 

loan is more economical. The buyer will save approximately 

​$enter your response here 

in interest.  

To determine which mortgage option is more economical in terms of paying less interest, we'll calculate the total amount of interest paid over the life of each loan using the formula for the monthly payment:

\[
PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

Where:
- $ P $ is the loan amount ($80,000),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the number of payments per year (12 for monthly payments),
- $ t $ is the term of the loan (in years).

We'll calculate the monthly payment for each loan, then compute the total payment over the loan period, and finally subtract the loan amount to find the total interest paid.

Let's calculate that now.Here are the results for both mortgage options:

1. **30-year loan at 7%:**
   - Monthly payment: \$532.24
   - Total interest paid: \$111,607

2. **15-year loan at 6.5%:**
   - Monthly payment: \$696.89
   - Total interest paid: \$45,439

**Interest savings**: By choosing the 15-year loan, the buyer would save approximately **\$66,168** in interest compared to the 30-year loan.

Therefore, **Option A** is correct: the 15-year loan at 6.5% is more economical, saving the buyer around **\$66,000** in interest.

Let me know if you'd like any further details, or if you have additional questions. Here are five related questions to consider:

1. How does increasing the down payment affect the interest paid over the loan term?
2. What would be the effect of paying an extra \$100 per month on either of these loans?
3. How would the total interest change if the 30-year loan had an interest rate of 6% instead of 7%?
4. Can refinancing during the term of the loan lead to further interest savings?
5. How does the loan amortization schedule differ between a 15-year and a 30-year loan?

**Tip**: Paying more than the required monthly payment on a mortgage can significantly reduce the total interest paid over time.

In terms of paying less in interest, which is more economical for an $80,000 mortgage: a 30-year fixed-rate at 7% or a 15-year fixed-rate at 6.5%? How much is saved in interest?

Determine which mortgage option is more economical in terms of paying less interest for an $80,000 loan: a 30-year fixed-rate at 7% or a 15-year fixed-rate at 6.5%. The buyer can save approximately $66,000 in interest with the 15-year loan. Includes step-by-step formula breakdown.

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