Latest Book Aptitude Question SOLUTION: $1000 is invested at4.8% compounded continuously, how long will it take for the account to reach $2500?

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(#M40036169) BOOK question Keep an EYE

$1000 is invested at4.8% compounded continuously, how long will it take for the account to reach $2500?

Asked In Book (10 years ago)

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Param Kothari  (10 years ago)

Standard formula for Compound Interest is FV = PV(1+i/n)^(n*t), where

FV = future value of the money, $2,500
PV = present value of the money, $1,000
i = annual interest rate, 4.8%
n = number of compounding periods per year, 1
t = number of years
therefore 2500 = 1500 (1+4.8/100)^t
(2500/1500) = (1.048)^t
2.5 = (1.048)^t
Take natural log of both the sides..
ln(2.5) = t * ln(1.048)
when we have exponent inside log, you need to bring it out as coefficient
therefore t = ln(2.5) /ln(1.048)
Type it in Google search (it will show calculator) and final answer is
19.54 years.

You can validate this answer by using same formula for FV (Future Value)
1000(1.048)^19.54 where 1000 is Present Value, 0.048 is 4.8% interest and t = time = 19.54 years. Enter this equation in google calculator and you will get FV = 2499.53638447 which equals to 2500.

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