# A sum of amount invested at certain rate of simple interest doubles itself in 8 years. What is the rate of interest?

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To solve, apply the formula of simple interest which is:

`A=P(1+rt)`

where

A - accumulated value after t years, P - initial amount, r - rate and

t - number of years

Since the amount doubles after 8 years, then A=2P and t=8.

`A=P(1+rt)`

`2P=P(1+r*8)`

`2P=P(1+8r)`

To simplify the equation, divide both sides by P.

`(2P)/P=(P(1+8r))/P`

`2=1+8r`

Then, isolate r. To do so, subtract both sides by 1.

`2-1=1+8r-1`

`1=8r`

And, divide both sides by 8

`1/8=(8r)/8`

`0.125=r`

To express the value of r in percent form, multiply it by 100,.

`r=0.125*100=12.5%`

**Hence, the rate of interest is 12.5 %.**

Answer :

Since the rate of interest denotes number of additional units of currency earned or paid for every 100 units of currency lent or borrowed as the case may be.

If the amount deposited or lent is Rs 100, and final amount received after certain number of years has to be Rs 200 (given that the sum doubles in certain number of years)

Interest earned = Amount - Principal = Rs 200 - Rs 100 = Rs 100

Number of years = 8 (given)

Rate = Interest/Time in years

= 100/8 = 12.5%.

Verify Rs 100 invested for 8 years at 12.5% will earn interest of

PTR = (100 x 8 x 0.125) = 100. Total Amount = Principal + Interest

= Rs 100 + Rs 100 = Rs 200.