# What is the rate of interest if an amount invested becomes three times after 8 years ( compound interest)

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An amount P invested at a rate of interest r for t years becomes an amount equal to A = P*(1 + r)^t.

The time in number of years has to be determined after which an amount becomes three times. Let the annual rate of interest be r.

=> 3P = P*(1 + r)^8

=> 3 = (1 + r)^8

Take the logarithm of both the sides

log 3 = log((1 + r)^8)

Use the property log a^b = b*log a

=> log 3 = 8*log (1 + r)

=> log (1 + r) = log 3/8

=> 1 + r = 10^(log 3/8)

=> r = 10^(log 3/8) - 1

=> r = 0.1472

**At an annual interest rate of 14.72% an amount becomes triple in 8 years.**

Let the Investment be I, Interest Rate R, Time T and Amount after time T be A

Then A = I*(1+R)^T

for T = 8, A = 3*I

3*I = I*(1+R)^8

3*I/I = (1+R)^8

3 = (1+R)^8

1+R = 3^(1/8)

1+R = 1.147203

R = 0.147203 = 14.7203%

*The rate of interest for an amount invested to become 3 times in 8 years is 14.7203%*