Question

The amount of $5000 is placed in savings account where interest is compounded continuously at the rate of 6% per year. How long will it take for this amount to triple?

Answer 1

Given Data -

• Principal Amount = P = $5000
• Interest Rate = r = 6% per year
• Triple amount = A =  3*5000 = $15000
• Time period = t = ?

Question - Time required to triple the amount ?

Let's first understand what is compond interest -Comound interest is calculated on initial principal which also includes all of the accumulated interest from the previous periods on deposite.Lets say we have principal amount of $500 and interest rate of 10% so at the end of the 1st year we will get amount of $550 (P*r*t/100 = 500*10*1/100) .Now for calculating amount for 2nd year we will take principal amount as $550 which is calculated at the end of the 1st year.So at the end of the second year we will get $55 (P*r*t/100 = 550*10*1/100) as interest amount so total amount at the end of the 2nd year will be $550+ $ 55 = $605.This is how compound interest is calculated.

Now coming to our question,

The generized formula for calculating number of years is,

A = P*e^rt

15000 = 5000*e^0.06*t

Dividing each sides by 5000,

3 = e^0.06*t

Taking natural log on both sides we will get,

ln(3) = 0.06t

Dividing each sides by 0.06

ln(3)/0.06 = t

t =18.31 years

Time required to triple the principal amount is 18.31 years.