Question

You're trying to save to buy a new $68,000 sports car. Currently, you have saved $36,840 which is invested at 4.9 percent annual interest. How many years will it be before you purchase the car, assuming the price of the car remains constant

Answer 1

Answer: Approximately 12.8 years.

Explanation:

Formula to calculate accumulated amount (compounded annually): $A=P(1+r)^t$ , where r= rate of interest , t= time

As per given, A= $68,000, P=$36,840 , r=4.9%= 0.049

To find : t

Substitute all values in formula , we get

$68000=36840(1+0.049)^t\\\\\Rightarrow\ \dfrac{68000}{36840}=(1.0.049)^t\\\\\Rightarrow\ 1.84582=(1.0.049)^t$

Taking log on both sides , we get

$\log(1.845819)=t\log(1.049)\\\\\Rightarrow\ t=\dfrac{\log(1.845819)}{\log(1.049)}\\\\\Rightarrow\ t=\dfrac{0.266189112}{0.020775488}=12.8126\approx12.8$

Hence, it it will take approximately 12.8 years.