Find the number of years

Algebra Level 2

You put your money in a bank which compounds interest at a fixed interest rate.
You notice that after 15 years, the amount of money is 2 times the principle.

How many years in total would it take for the amount to be 8 times the principle?

60 years 20 years 35 years 45 years

Ronak Sahai by Ronak Sahai , 20, India

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2 solutions

Ronak Sahai
Mar 17, 2017

1st Case

2 P = P [ 1 + R 100 ] 1 5 2P = P[1 + \frac{R}{100}]^15

2 = [ 1 + R 100 ] 1 5 2 = [1 + \frac{R}{100}]^15

2nd Case

8 P = P [ 1 + R 100 ] n 8P = P[1 + \frac{R}{100}]^n

8 = [ 1 + R 100 ] n 8 = [1 + \frac{R}{100}]^n

2 3 = [ 1 + R 100 ] n 2^{3} = [1 + \frac{R}{100}]^n

From 1st Case

( [ 1 + R 100 ] 15 ) 3 = [ 1 + R 100 ] n ( [1 + \frac{R}{100} ]^{15} )^{3} = [1 + \frac{R}{100}]^n

[ 1 + R 100 ] 45 = [ 1 + R 100 ] n [1 + \frac{R}{100}]^{45} = [1 + \frac{R}{100}]^n

45 = n

Answer = 45 years

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Richard Costen
Mar 19, 2017

The principal is doubled every 15 years. To end up with 8 times as much money, it must be doubled 3 times. 2 3 = 8 2^3=8 . This means going through 15 years 3 times, or 45 years.

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