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**.