Question

You plan to buy your "dream car" when you graduate in 12 months.
The cost of the car at that time will be $59,000 .
How much do you have to invest each month, starting next month, for 29 months to exactly pay for the car if your investments earn 5.00% APR (compounded monthly)?

Calculate your answer to the nearest dollar.

Answer 1

The question says the cost of the car in 12 months would be $59,000, but the investments are being made for 29 months. So it is being assumed here that the cost of the car remains $59,000 at the end of 29 months too.

To calculate the investment to be made monthly, we can use the formula for calculating the future value of a series of cash flows:

-------- (1)

FV = CF [((1+r) - 1)/r]

where,

• FV is the future value of the series of cash flows
• CF is the cash which is invested periodically
• r is the interest rate
• N is the period of investment

Rearranging the above formula, we get the following formula to calculate the cash to be invested periodically:

---------- (2)
We have the following data:

CF = (FV *r)/((1+r)^- 1

1. FV: $59,000
2. N: 29 months
3. Compounding frequency: Monthly
4. APR: 5.0%; however, since compounding is being done monthly, r will be 5% / 12 = 0.417%

Substituting these values in formula (2),

CF = ($59000 * 0.00417) / [ (1.00417^29) -1]

= $ 246 / 0.1283

= $1,918

Hence, $1,918 will have to invested every month for 29 months at 5% APR to accumulate $59,000.

Similarly, ff the car were to be bought at the end of 12 months, then $4,805 will have to be invested every month for 29 months at 5% APR to accumulate $59,000.