Question

Al Derover wants to buy a used jeep in five years. He estimates the cost will be $12,000. If he invests $8,500 now at a rate of 10% compounded semiannually, will he have enough money to buy the jeep at the end of five years?

Answer 1

Answer: Yes he will have enough money to buy the jeep at the end of five years.

Step-by-step explanation:

Given: Al Derover invests $8,500 now at a rate of 10% compounded semiannually for five years.

Principal amount P= $8500

Rate of interest r =10% semiannually= $\frac{10}{2}=5\%=0.05$

Number of periods n=$2\times5=10$

Now, the Compound amount (A) after n periods is given by:-

$A=P(1+r)^n\\\Rightarrow\ A=8500(1.05)^{10}\\\Rightarrow\ A=13845.6043276\approx=\ 13845.60$

Clearly, $13845.60>$12,000

Hence, Yes he will have enough money to buy the jeep at the end of five years.