Romesh borrowed a sum of Rs 245760 at 12. 5% per annum, compounded annually. On the someday, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.

Explanation

Principal `(P)=Rs. 245760`
Rate `(R)=12.5%=25/2%` p.a
Time `(n)=2` years
`A=P(1+R/100)^n`
`A=245760(1+25/(2times100))^2`
`A=245760(1+1/8)^2`
`A=245760(9/8)^2`
`A=245760times9/8times9/8`
`A=311040`
`CI=A-P=Rs. 311040-Rs. 245760=Rs. 65280`
For semi-annually,
Rate `(R)=25/4%` half-yearly
Time`(t)=2` years
Number of times interest applied `(n)=2`
`A=P(1+R/100)^(nt)=245760(1+25/(4times100))^(2times2)`
`A=245760(1+1/16)^4`
`A=245760(17/16)^4`
`A=245760times17/16times17/16times17/16times17/16`
`A=313203.75`
`CI=A-P=Rs. 313203.75-Rs. 245760=Rs. 67443.75`
Gain`=Rs. 67443.75−Rs. 65280=Rs. 2163.75`
`therefore` Romesh gain `Rs. 2163.75` after `2` years.