Question

You are looking to purchase a new car, and you expect to have annual maintenance costs to keep it running. According to your calculations, you expect to incur $150 maintenance costs in the first year and expect the costs to increase by $100 for the next 7 years. You plan to keep the car for 8 years in total. How much money should you have in your savings account today, so that you do not have to worry about maintenance? The savings account pays 2% per year, compounded annually.

Answer 1

I should have $11,554.94 in my savings account today.

Step-by-step explanation:

This can be calculated using the formula for calculating the present value (PV) of a growing annuity as follows:

PVga = (P / (r - g)) * (1 – ((1 + g) / (1 + r))^n) .................... (1)

Where;

P = maintenance costs in the first year = $150

r = interest per year = 2%, or 0.02

g = growth rate of maintenance costs = Expected annual increase in maintenance costs / maintenance costs in the first year = $100 / $150 = 0.666666666666667

n = useful life = 8

Substituting the values into equation (1), we have:

PVga = (150 / (0.02 - 0.666666666666667)) * (1 - ((1 + 0.666666666666667) / (1 + 0.02))^8)

PVga = 11,554.94

Therefore, I should have $11,554.94 in my savings account today.