Question

A wealthy businessman invests $10,000 and expects a 6.75% rate of return annually. How many years will it take the investment to reach at least $15,000 in value?Round your answer to the nearest number of years. Do not include units on your answer.

Answer 1

Answer:

Given that,

A wealthy businessman invests $10,000.

It expects a 6.75% rate of return annually.

To find: the number of years it take the investment to reach at least $15,000 in value.

Explanation:

we know that,

Amount invested at r% rate of interest after t years is,

$A=P(1+\frac{r}{100})^t$

where P is the initial investment.

Substitute the values we get,

$15000=10000(1+\frac{6.75}{100})^t$

we get,

$\frac{3}{2}=1.0675^t$$1.5=1.0675^t$

we get,

$\log_{1.0675}(1.5)=t$

Calculating this we get,

$t=6.207$

Round to the nearest number of years.

we get,

$t=6$

6 years will it take the investment to reach at least $15,000 in value.

Answer is: 6 years will it take the investment to reach at least $15,000 in value