Question
If you buy a car where you give a down payment of $ 998 and the payment will be $ 465 monthly for 5 ½ years at an interest rate of 8.5% per annum computed monthly. What was the sale price?
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Answer to a math question If you buy a car where you give a down payment of $ 998 and the payment will be $ 465 monthly for 5 ½ years at an interest rate of 8.5% per annum computed monthly. What was the sale price?
Adonis
4.4101 Answers
Solution:
1. Given:
- Down payment: USD 998
- Monthly payment: USD 465
- Loan term: 5.5 years or 66 months
- Annual interest rate: 8.5% (monthly rate= \frac{8.5}{12}
2. Use the formula for the present value of an annuity to find the loan amount:
\text{Loan Amount} = P \times \frac{1 - (1 + r)^{-n}}{r}
where
-P
-r
-n
3. Substitute and compute:
\text{Loan Amount} = 465 \times \frac{1 - (1 + 0.0070833)^{-66}}{0.0070833}
4. Calculate the value:
\text{Loan Amount}\approx465\times50.9965\approx24446.96
5. Add the down payment to get the total sale price:
\text{Sale Price} = \text{Loan Amount} + \text{Down Payment}
\text{Sale Price}=24446.96+998
\text{Sale Price}=25444.96
1. Given:
- Down payment: USD 998
- Monthly payment: USD 465
- Loan term: 5.5 years or 66 months
- Annual interest rate: 8.5% (monthly rate
2. Use the formula for the present value of an annuity to find the loan amount:
where
-
-
-
3. Substitute and compute:
4. Calculate the value:
5. Add the down payment to get the total sale price:
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