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?

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Adonis

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95 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}

percent = 0.70833% = 0.0070833)

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

-

is the monthly payment (USD 465)

-

is the monthly interest rate (0.0070833)

-

is the total number of payments (66)

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

USD

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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?

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?

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