The number of years in which the simple interest on a sum of money will be equal to the principal depends on the rate of interest. Using the simple interest formula:
SI=P×R×T100SI=\frac{P\times R\times T}{100}SI=100P×R×T
where SISISI is the simple interest, PPP is the principal, RRR is the rate of interest per annum, and TTT is the time in years. If the simple interest equals the principal (SI=PSI=PSI=P), then:
P=P×R×T100P=\frac{P\times R\times T}{100}P=100P×R×T
Dividing both sides by PPP (assuming P≠0P\neq 0P=0):
1=R×T100 ⟹ T=100R1=\frac{R\times T}{100}\implies T=\frac{100}{R}1=100R×T⟹T=R100
For example, if the rate of interest is 12.5%12.5%12.5% per annum, then:
T=10012.5=8 yearsT=\frac{100}{12.5}=8\text{ years}T=12.5100=8 years
So, the simple interest will equal the principal in 8 years at 12.5% interest rate
. Another example: If you want to find the time when the interest on Rs. 2,500 at 3% per annum equals the interest on Rs. 1,500 at 7% per annum for 5 years, you calculate the interest on Rs. 1,500 first:
I=1500×7×5100=525I=\frac{1500\times 7\times 5}{100}=525I=1001500×7×5=525
Then set this equal to the interest on Rs. 2,500 at 3% for TTT years:
525=2500×3×T100 ⟹ T=7 years525=\frac{2500\times 3\times T}{100}\implies T=7\text{ years}525=1002500×3×T⟹T=7 years
So, in this case, the time is 7 years
. In summary, the formula to find the number of years when simple interest equals the principal is:
T=100RT=\frac{100}{R}T=R100
where RRR is the annual interest rate in percent.
