Question

How long will it take money to double if it is invested at the following​ rates? ​(A) 4.8​% compounded monthly ​(B) 10.5​% compounded monthly

Answer 1

Answer A.

Amount invested = $1
Desired sum = $2

Annual interest rate = 4.80%
Monthly interest rate = 0.40% (4.80% / 12)

Let it will take n months to double the investment

Amount invested * (1 + Monthly interest rate)^Period = Desired sum
$1 * 1.004^n = $2
1.004^n = 2
n * ln(1.004) = ln(2)
n = 173.63

Number of months = 173.63
Number of years = 173.63 / 12
Number of years = 14.47 years

Answer B.

Amount invested = $1
Desired sum = $2

Annual interest rate = 10.50%
Monthly interest rate = 0.875% (10.50% / 12)

Let it will take n months to double the investment

Amount invested * (1 + Monthly interest rate)^Period = Desired sum
$1 * 1.00875^n = $2
1.00875^n = 2
n * ln(1.00875) = ln(2)
n = 79.56

Number of months = 79.56
Number of years = 79.56 / 12
Number of years = 6.63 years