Asked by mula
misty has the choice of taking out a 25-year loan for $105,00 at 3.8% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. if she would pay a total of $57,810 in interest on the 25-year loan, how much in total would she pay in interest on the 20-year loan?
$ 57,810
$105,000
$ more than $57,810 but less than $105,000
$ less than $57,810
$ 57,810
$105,000
$ more than $57,810 but less than $105,000
$ less than $57,810
Answers
Answered by
GPT-4o mini
To find out how much Misty would pay in total interest on the 20-year loan, we first need to calculate the total payments for the 25-year loan and then use that information to evaluate the 20-year loan.
1. **Calculating Total Payments for the 25-Year Loan**:
- Principal Amount: $105,000
- Interest Paid on 25-Year Loan: $57,810
- Total Amount Paid = Principal + Interest
- Total Amount Paid for the 25-Year Loan = $105,000 + $57,810 = $162,810
2. **Understanding the Impact of Loan Duration**:
- The 20-year loan will have a higher monthly payment because it is being paid off in a shorter timeframe.
- With a higher monthly payment over a shorter duration, the expenditure on interest will generally be lower.
Given that she pays $57,810 in interest over 25 years, for the 20-year loan scenario (which is effectively paying off the principal faster), the total interest will be less than $57,810 because you are paying off the loan sooner and accruing less interest overall.
Thus, the options you provided can be analyzed as follows:
- $57,810 (the total interest for the 25-year loan)
- $105,000 (the principal, which is not the interest)
- $ more than $57,810 but less than $105,000 (impossible)
- $ less than $57,810 (this is likely)
**Conclusion**:
The total interest paid on the 20-year loan will be **$ less than $57,810**.
1. **Calculating Total Payments for the 25-Year Loan**:
- Principal Amount: $105,000
- Interest Paid on 25-Year Loan: $57,810
- Total Amount Paid = Principal + Interest
- Total Amount Paid for the 25-Year Loan = $105,000 + $57,810 = $162,810
2. **Understanding the Impact of Loan Duration**:
- The 20-year loan will have a higher monthly payment because it is being paid off in a shorter timeframe.
- With a higher monthly payment over a shorter duration, the expenditure on interest will generally be lower.
Given that she pays $57,810 in interest over 25 years, for the 20-year loan scenario (which is effectively paying off the principal faster), the total interest will be less than $57,810 because you are paying off the loan sooner and accruing less interest overall.
Thus, the options you provided can be analyzed as follows:
- $57,810 (the total interest for the 25-year loan)
- $105,000 (the principal, which is not the interest)
- $ more than $57,810 but less than $105,000 (impossible)
- $ less than $57,810 (this is likely)
**Conclusion**:
The total interest paid on the 20-year loan will be **$ less than $57,810**.