The difference between the compound interest and the simple interest for 2 years at 5% per annum is Re 1. Find the sum.
Answers
Step-by-step explanation:
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Rs. 11. What is the sum?
Let the Principal = Rs 100
Rate of interest = 5% per annum
Time = 2 years
Simple interest = Rs 100 ×( 5/100) × 2 = Rs 10
Amount after 2 years when Rs 100 is put at compound interest at 5% per annum compounded annually = 100[1 + (5/100)]² = 100( 21/20)² = 441/400 × 100 = 441/4 = 110.25
CI for two years = Rs 110.25 — Rs 100 = Rs 10.25
Difference in CI and SI in two years = Rs 10.25 — Rs 10 = Rs 0.25
If difference in CI and SI is Rs 0.25 then the Principal = Rs 100
If difference in CI and SI is Re 1 then the principal = Rs 100/0.25 = Rs 400
If difference in CI and SI is Rs 11 then the Principal = Rs 400 × 11 = Rs 4400.
Verfication
SI in 2 years = Rs 4400 × (5/100) × 2 = Rs 440
Amount in two years = 4400 (21/20)² = Rs 4851
CI in two years = Rs 4851 — Rs 4400 = Rs 451
Difference in CI and SI = Rs 451 — Rs 440 = Rs 11.