A person invested $500 each in two different schemes S1 and S2. The re

Solution

• A person invested $500 each in two different schemes S1 and S2.
• The return on investment will be calculated on compound interest, compounded annually

• The difference between the interest earned, from S1 for the 2nd year, and from S2 for the 3rd year

• The amount invested (given as $500 each in S1 and S2)
• The rate of interest for S1 and S2

• As per the information given in statement 1, S1 amounts to $525 at the beginning of year 2

o Beginning of year 2 indicates the amount (principal + interest) at the end of year 1
• Now, we know for a span of 1-year, simple interest and compound interest will be same (if compounding is done annually)
• Hence, if the rate of interest is r1, we can write \(500 * \frac{r1}{100} = 525\)

o From this we can find out the value of r1 = 5
• But we don’t have sufficient information to figure out the value of r2

• As per the information given in statement 2, at the end of year 1, S2 earns $25 more interest compared to S1
• If we assume the rate of interests for S1 and S2 to be r1 and r2 respectively, then we can write

o \(500 * \frac{r2}{100} – 500*\frac{r1}{100} = 25\)
Or, 5r2 – 5r1 = 25
Or, r2 – r1 = 5
• But from this equation, we can’t find out the exact values of r1 and r2 individually

• r1 = 5
• r2 – r1 = 5

o Hence, r2 = 5 + r1 = 5 + 5 = 10