Principal Sum Calculation for Simple Interest
The problem asks for the initial sum of money (Principal, P) that will grow to a total amount (A) of ₹2,400 after 4 years (T) at a simple interest rate (R) of 5% per annum.
Simple Interest Formula
The formula for the Amount (A) in simple interest is:
A = P + SI
Where SI (Simple Interest) is calculated as:
SI = $ \frac{P \times R \times T}{100} $
Substituting the SI formula into the Amount formula:
A = P + $ \frac{P \times R \times T}{100} $
Factor out P:
A = P $ \left(1 + \frac{R \times T}{100}\right) $
Applying the Formula
We are given:
- Amount (A) = ₹2,400
- Rate (R) = 5%
- Time (T) = 4 years
Substitute these values into the formula:
₹2,400 = P $ \left(1 + \frac{5 \times 4}{100}\right) $
₹2,400 = P $ \left(1 + \frac{20}{100}\right) $
₹2,400 = P $ \left(1 + 0.20\right) $
₹2,400 = P $ (1.20) $
Solving for Principal (P)
To find the principal sum (P), rearrange the equation:
P = $ \frac{₹2,400}{1.20} $
P = $ \frac{24000}{12} $
P = ₹2,000
Conclusion
The sum of money that will amount to ₹2,400 at 5% simple interest in 4 years is ₹2,000.
Similar Questions
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- Sapna invested ₹21,900 on simple interest, partly at 14% per annum and partly at 10% per annum. If she earns equal interests from the two investments after 2 years, then find the sum invested at 14% per annum (in ₹).
- Find the simple interest (in ₹) on ₹1,200 at an interest rate of 4% per month for 11 months.
- A man purchases a washing machine for $₹12,000$. He pays $₹2,000$ at first and the rest after $1\text{ year}$, on which he is charged a simple interest at the rate of $10\%$ per year. The total amount he pays for the washing machine is:
- Sapna invested ₹21,700 on simple interest, partly at 3% per annum and partly at 12% per annum. If she earns equal interests from the two investments after 7 years, then find the sum invested at 3% per annum (in ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- Sapna invested ₹20,300 on simple interest, partly at the rate of 8% per annum and partly at the rate of 6% per annum. If she earns equal interests from the two investments after 6 years, then find the sum invested at the rate of 8% per annum (in ₹).
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 5 February 2024 and withdrawn on 6 April 2024.
- The simple interest on a certain sum for 3 years at 8% per annum is ₹96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.
Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
