The ratio of simple interest earned by a certain amount at the same rate of interest for two different time periods is directly proportional to the ratio of those time periods. Using the simple interest formula:
SI=P×R×T100SI=\frac{P\times R\times T}{100}SI=100P×R×T
where PPP is the principal, RRR is the rate of interest, and TTT is the time, if the principal and rate remain the same, the ratio of simple interest earned for times T1T_1T1 and T2T_2T2 is:
SI1SI2=P×R×T1/100P×R×T2/100=T1T2\frac{SI_1}{SI_2}=\frac{P\times R\times T_1/100}{P\times R\times T_2/100}=\frac{T_1}{T_2}SI2SI1=P×R×T2/100P×R×T1/100=T2T1
Examples:
- For 6 years and 9 years, the ratio of simple interest is 6:9=2:36:9=2:36:9=2:3
- For 9 years and 12 years, the ratio is 9:12=3:49:12=3:49:12=3:4
- For 4 years and 8 years, the ratio is 4:8=1:24:8=1:24:8=1:2
- For 6 years and 4 years, the ratio is 6:4=3:26:4=3:26:4=3:2
In summary, the ratio of simple interest earned for different time periods at the same principal and rate of interest equals the ratio of those time periods.
