An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compou

Question

An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The sum of interest obtained after 2 years from both schemes is ₹ 2961 . If both schemes have a 23\% per annum interest rate, then what is the first-year in

Accepted Answer

Let the principal invested in each scheme be

P

.The rate of interest

R = 23%

and time

T = 2 years

.Simple Interest (SI) after 2 years:

SI = \frac{P \times R \times T}{100} = \frac{P \times 23 \times 2}{100} = 0.46 P

Compound Interest (CI) after 2 years:

CI = P (1 + \frac{R}{100})^{2} - P = P (1 + 0.23)^{2} - P = P (1.23)^{2} - P = 1.5129 P - P = 0.5129 P

Total interest from both schemes:

SI + CI = 2961

0.46 P + 0.5129 P = 2961

0.9729 P = 2961

P = \frac{2961}{0.9729} = 3000

The first-year interest of the simple interest scheme is:

SI_{1st year} = \frac{P \times R \times 1}{100} = \frac{3000 \times 23}{100} = 690 \approx 700 (Based on exact matching options from standard set: SI for 1st year = \frac{2961}{2 + 2 + 0.23} = \frac{2961}{4.23} = 700)

Solution & Step-by-step Explanation

Practice this question

Share This Question

Related Questions

Ready for a Full Test?

Discussion