Question

Stephen plans to purchase a car 5 years from now. The car will cost $43,011 at that time. Assume that Stephen can earn 7.11 percent (compounded monthly) on his money. How much should he set aside today for the purchase?

Answer 1

$30,174.74

Explanation:

The computation of present value is shown below:-

Future value = Present value × (1 + Rate of interest ÷ 1200)^12 × time period

$43,011 = Present value × (1 + 7.11 ÷ (12 × 100)^(12 × 5)

$43,011 = Present value × (1 + 7.11 ÷ 1,200)^60

$43,011 = Present value × (1 + 0.005925 )^60

Present value = $43,011 ÷ (1 + 0.005925 )^60

= $43,011 ÷ (1.005925 )^60

= $43,011 ÷ 1.425397857

= $30,174.73317

or

= $30,174.74

Therefore for computing the present value we simply applied the above formula.

We also attached the spreadsheet for better understanding

In compounded monthly, the interest rate is divided by 12 months and the time period is multiplied by 12 months and the same is to be considered