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Carmen plans to buy a used truck by paying a $2000 down payment and financing the

remaining $18000 with a 3-year auto loan at 4% annual interest compounding monthly. What is the total cost of the truck including all payments and down payment? rounded to 2 decimal places. Do not include the $ symbol.

Carmen plans to buy a used truck by paying a $2000 down payment and financing the-example-1
User Reducer
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1 Answer

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Explanation:

To calculate the total cost of the truck including all payments and down payment, we can use the formula for the future value of an annuity due:

FV = PMT × (((1 + r/n)^(n×t) - 1) / (r/n)) + PV × (1 + r/n)^(n×t)

where:

- FV is the future value of the annuity due (the total cost of the truck including all payments and down payment)

- PMT is the monthly payment

- r is the annual interest rate (4%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (3)

- PV is the present value of the annuity due (the amount financed after the down payment)

First, we need to calculate the monthly payment:

PMT = (r/n) × PV / (1 - (1 + r/n)^(-n×t))

PV = $18,000 - $2,000 = $16,000

PMT = (0.04/12) × 16000 / (1 - (1 + 0.04/12)^(-12×3)) = **$470.98**

Now we can calculate the future value of the annuity due:

FV = PMT × (((1 + r/n)^(n×t) - 1) / (r/n)) + PV × (1 + r/n)^(n×t)

FV = 470.98 × (((1 + 0.04/12)^(12×3) - 1) / (0.04/12)) + 16000 × (1 + 0.04/12)^(12×3) = **$19,981.63**

Therefore, the total cost of the truck including all payments and down payment is **$21,981.63**.

User Kris Randall
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