Question

If $50 is invested at 6 percent interest. How long will it take to double?

Answer 1

16 years and 8 months with simple interest earned
11 years and 11 months with compound interest earned

Explanation:

The time will differ between an investment with compound interest and with simple interest. It will happen sooner with Compound interest.

Simple interest:

In order to double in value, the interest must be `$50`

`SI =(PRT)/100" "rarr (50 xx 6 xx T)/100 =50`

`T = (100xx50)/(50xx6)`

`T= 100/6 = 16.6666 = 16 2/3` years

16 years and 8 months to double with simple interest

Compound interest

In order to double, the Amount must be `$100`

`A = P(1+R/100)^n`

`50(1+0.06)^n= 100`

`(1.06)^n= 100/50 = 2`

`nlog(1.06) = log2`

`n= log2/log1.06`

`n = 11.89` years

`n~~ 11` years and 11 months