Question

If you invest P dollars and you want the investment to grow to A dollars in t years, the interest rate that must be earned if interest is compounded annually is given by the formula r = t √ A P − 1 If you invest $ 1500 and want to have $ 6000 in 8 years, what interest rate must be earned? Round to at least 1 decimal place. You need an interest rate of at least 1.19 Incorrect percent.

Answer 1

Answer: 18.92%

Explanation:

The formula to find the compound amount :-

$A=P(1+r)^t$, where P is the Principal amount, r is the rate of interest and t is the time period.

Given : P= $1500

A = $6000

Time = 8 years

Then $6000=1500(1+r)^8$

i.e. $(1+r)^8=\dfrac{6000}{1500}=4$

i

Taking natural log on both sides , we get

$\Rightarrow\ 8\ln(1+r)=\ln(4)\\\\\Rightarrow\ \log(1+r)=\dfrac{\log4}{8}=\dfrac{1.38629436112}{8}=0.17328679514\\\\\Rightrarrow\ 1+r=e^{0.17328679514}\\\\\Rightarrow\ 1+r=1.189207115\\\\\Rightarrow\ r=1.189207115-1=0.189207115\\\\\Rightarrow\ r\approx0.1892\approx18.92\%$