The difference between the compound interest and the simple interest on a certain sum of money for 2 years at 11% per annum is Rs. 363. Find the sum.
1.33,000
2.31,000
3.30,000
4.32,000
Answers
Answer:
The sum of money = Rs 30,000
Step-by-step explanation:
➤ Given that:
- The difference between the compound interest and simple interest = Rs 363
- Time = 2 years
- Rate of interest = 11% per annum
Let us assume that the certain sum of money be x.
➤ Formula to find compound interest:
- C.I. = A - p
- C.I. = p(1 + 0.01r)ᵗ - p
Where,
- C.I. = Compound interest
- A = Amount
- p = Principal/Sum of money
- r = Rate of interest
- t = Time
- 0.01 = 1/100
➤ Formula to find simple interest:
S.I. = (p × r × t × 0.01)
Where,
- S.I. = Simple interest
- p = Principal/Sum of money
- r = Rate of interest
- t = Time
- 0.01 = 1/100
★ Finding the Sum of money/Principal:
C.I. - S.I. = 363
→ p(1 + 0.01r)ᵗ - p - (p × r × t × 0.01) = 363
→ x(1 + 0.11)² - x - (x × 11 × 2 × 0.01) = 363
→ x(1.11)² - x - 0.22x = 363
→ 1.2321x - 1.22x = 363
→ 0.0121x = 363
→ x = 363/0.0121
→ x = 30000
∴ Sum of money = Rs 30,000
Answer:-
The sum of money = Rs 30,000
Step-by-step explanation:
➤ Given that:
- The difference between the compound interest and simple interest = Rs 363
- Time = 2 years
- Rate of interest = 11% per annum
Let us assume that the certain sum of money be x.
➤ Formula to find compound interest:
- C.I. = A - p
- C.I. = p(1 + 0.01r)ᵗ - p
Where,
- C.I. = Compound interest
- A = Amount
- p = Principal/Sum of money
- r = Rate of interest
- t = Time
- 0.01 = 1/100
➤ Formula to find simple interest:
S.I. = (p × r × t × 0.01)
Where,
- S.I. = Simple interest
- p = Principal/Sum of money
- r = Rate of interest
- t = Time
- 0.01 = 1/100
★ Finding the Sum of money/Principal:
C.I. - S.I. = 363
→ p(1 + 0.01r)ᵗ - p - (p × r × t × 0.01) = 363
→ x(1 + 0.11)² - x - (x × 11 × 2 × 0.01) = 363
→ x(1.11)² - x - 0.22x = 363
→ 1.2321x - 1.22x = 363
→ 0.0121x = 363
→ x = 363/0.0121
→ x = 30000