Final answer:
To find the sum, we need to calculate the compound interest and the simple interest separately and then find the difference. Using the formula for compound interest, we can calculate the sum to be approximately 408.52 rupees for a certain amount of money at 16% per annum compounded annually for 27 months.
Step-by-step explanation:
To find the sum, we need to calculate the compound interest and the simple interest separately and then find the difference. Let's start with the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A = the future amount (including interest)
- P = the principal (initial amount)
- r = the annual interest rate (as a decimal)
- n = the number of times interest is compounded per year
- t = the number of years
In this case, the annual interest rate is 16% (0.16 as a decimal), the number of times interest is compounded per year is 1 (compounded annually), and the number of years is 27/12 = 2.25 (since 27 months is equal to 2.25 years). Let's calculate the compound interest:
616 = P(1 + 0.16/1)^(1*2.25)
Simplifying this equation, we find:
P = 616 / (1 + 0.16/1)^(1*2.25)
Using a calculator, we can find that P is approximately 408.52 rupees.