Question

the maintenance cost for a car this year is expected to be $500. the cost will increase $65 each year for the subsequent 9 years. the interest is 4% compounded annually. the future worth of maintenance for the car over the full 10 years is nearest to:

Answer 1

To calculate the future worth of the maintenance cost for the car over the full 10 years, consider the increasing cost each year and the compounded interest.

The future worth is approximately $6,295.29.

To calculate the future worth of the maintenance cost for the car over the full 10 years, we need to consider the increasing cost each year and the compounded interest.

First, let's calculate the increasing cost of maintenance for each year:

1. Year 1: $500
2. Year 2: $500 + $65 = $565
3. Year 3: $565 + $65 = $630
4. Continuing this pattern, we can calculate the costs for all 10 years:
5. Year 4: $630 + $65 = $695
6. Year 5: $695 + $65 = $760
7. Year 6: $760 + $65 = $825
8. Year 7: $825 + $65 = $890
9. Year 8: $890 + $65 = $955
10. Year 9: $955 + $65 = $1,020
11. Year 10: $1,020 + $65 = $1,085

Next, let's calculate the future worth of the maintenance costs with the 4% compounded interest.

We can use the future value of an ordinary annuity formula:

Future Worth = Payment [(1 + r)^n - 1] / r

Where:

• Payment = $500
• r = 4% = 0.04
• n = 10

Plugging in these values, we get:

Future Worth = $500 [(1 + 0.04)^10 - 1] / 0.04

Solving this equation, the future worth of the maintenance costs over the full 10 years is approximately $6,295.29.