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

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.

Step-by-step explanation:

we know that,

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

`A=P(1+(r)/(100))^t`

where P is the initial investment.

Substitute the values we get,

`15000=10000(1+(6.75)/(100))^t`

we get,

`(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