Answer:
Principal = Rs. 5000
Interest Rate = 10%
Explanation:
- Simple Interest Formula is
SI = P x n x r/100
where P = principal, n = number of years and r = interest rate in %
- We have SI = 1000, n= 2 with r and P to be determined
- The simple interest for 2 years = 1000
Since simple interest is calculated on the principal and remains the same each year,
First year interest = 1000/2 = 500
Second year interest = 1000/2 = 500
- Compound Interest Formula:
CI = P(1+r/100) - P
- Compound interest is computed on the principal plus interest each year
- First year compound interest is calculated on the Principal = 500
- The interest for the next year = 1050 - 500 = 550
- The additional Rs. 50 comes from the interest calculated on the first year's interest of 500
- Therefore rate of interest = 50/500 = .10 = 10%
Computation of P and r
- Since simple interest for 2 years is P x n x r/100 we have
1000 = P x 2 x 10/100 = 0.2P
- Therefore principal P = 1000/0.2 = Rs. 5000
- Answer: Principal is Rs. 5000 and interest rate is 10%
- Cross-check
- Principal of 1000 and interest rate of 10% for 2 years gives:
SI = 5000 x 2 x 10/100 = 1000
- CI = 5000(1 + 10/100)² - 5000
=5000(1.1)² - 5000
= 5000(1.21) - 5000
= 6050 - 5000 = 1050
So calculations check out