Calculating Original Sum for Compound Interest
The question asks for the original sum (principal) invested, given the final amount, the compound interest rate, and the time period.
Compound Interest Formula
The formula for compound interest is:
$ A = P \left(1 + \frac{r}{100}\right)^n $
Where:
- $A$ = Final Amount (₹1,815)
- $P$ = Principal Sum (Original Investment)
- $r$ = Annual Interest Rate (10%)
- $n$ = Number of Years (2)
Solving for the Principal (P)
We need to rearrange the formula to find $P$:
$ P = \frac{A}{\left(1 + \frac{r}{100}\right)^n} $
Given Values
- $A = ₹1,815$
- $r = 10\%$
- $n = 2$
Calculation Steps
- Calculate the term $(1 + \frac{r}{100})$: $ 1 + \frac{10}{100} = 1 + 0.10 = 1.10 $
- Calculate the denominator $(1.10)^n$: $ (1.10)^2 = 1.21 $
- Substitute the values into the rearranged formula for $P$: $ P = \frac{1815}{1.21} $
- Perform the division: $ P = 1500 $
Conclusion
The original sum invested was ₹1,500.00.
Similar Questions
- A sum of ₹20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the compound interest.
- A sum is invested at compound interest payable annually. The interest in two successive years was ₹225 and ₹236.25. Find the rate of interest.
- A sum was invested for 3 years on compound interest at 6%, 12% and 18% in first, second and third year respectively. The sum amounts to ₹20,000 in 3 years. Find the principal amount.
- An amount doubles itself at compound interest in five years. In how many years will it amount to sixteen times itself?
- How much amount of money (in ₹) at compound interest will amount to ₹5,000 in 3 years if the rate of interest is 2% for the $1^\text{st}$ year, 3% for the $2^\text{nd}$ year and 4% for the $3^\text{rd}$ year?
Find the total amount (in ₹) on ₹4500 at 12% per annum for 2 years and 8 months compounded annually.
A sum of money becomes $₹6,400$ in $2\text{ years}$ and $₹8,100$ in $4\text{ years}$ on compound interest. Find the rate of compound interest.
- Find the compound interest on ₹7,500 at 4% per annum for 2 years.
- The compound interest on ₹20,000 at 8% per annum is ₹3,328. The period in years is:
- Find the compound interest when the principle is ₹6,000 at an interest of 10% per annum for 2 years.
Important Questions from Compound Interest
A person borrowed Rs. 10000 on compound interest at the rate of 40 percent per annum. If the interest is compounded half yearly, then what will be the amount to be paid after 1.5 years?
The difference between the compound interest (compounding annually) and the simple interest on a sum of money at the rate of 40 per cent per annum for 2 years is Rs. 2400. What is the amount?
In how many years will a sum of Rs.1875 amount to Rs.2187 at 8 percent p.a. compound interest?
A sum of money has increased by 45% in 9 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
At a certain rate of compound interest a certain sum amounts to Rs. 64800 in 4 years and Rs. 93312 in 6 years. What is the compound interest earned in fifth year?
