What is the compound interest on Rs. 8400 for 2 years at 10% per annum compounded annually?
Rs. 1764
Calculating Compound Interest on Rs. 8400
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. This means that in each subsequent period, the interest earned is added to the principal, and the interest for the next period is calculated on this new, larger principal.
To calculate the compound interest on Rs. 8400 for 2 years at 10% per annum compounded annually, we can use the formula for the amount (A) under compound interest:
\(\text{A} = \text{P}\left(1 + \frac{\text{R}}{100}\right)^n\)
Where:
- P is the principal amount (Rs. 8400)
- R is the annual interest rate (10%)
- n is the number of years (2 years)
First, let's calculate the total amount after 2 years:
\(\text{A} = 8400\left(1 + \frac{10}{100}\right)^2\)
\(\text{A} = 8400\left(1 + 0.10\right)^2\)
\(\text{A} = 8400\left(1.10\right)^2\)
\(\text{A} = 8400 \times 1.21\)
\(\text{A} = 10164\)
So, the total amount after 2 years is Rs. 10164.
To find the compound interest (CI), we subtract the original principal from the total amount:
\(\text{CI} = \text{A} - \text{P}\)
\(\text{CI} = 10164 - 8400\)
\(\text{CI} = 1764\)
Thus, the compound interest on Rs. 8400 for 2 years at 10% per annum is Rs. 1764.
Compound Interest Calculation Steps
Alternatively, we can calculate the interest year by year:
-
Year 1:
- Interest = Principal × Rate × Time
- Interest for Year 1 = \(8400 \times \frac{10}{100} \times 1 = 840\)
- Amount at the end of Year 1 = Principal + Interest = \(8400 + 840 = 9240\)
-
Year 2:
- The principal for Year 2 is the amount at the end of Year 1, which is Rs. 9240.
- Interest for Year 2 = Principal for Year 2 × Rate × Time
- Interest for Year 2 = \(9240 \times \frac{10}{100} \times 1 = 924\)
- Amount at the end of Year 2 = Amount at end of Year 1 + Interest for Year 2 = \(9240 + 924 = 10164\)
Total Compound Interest = Interest for Year 1 + Interest for Year 2
\(\text{Total CI} = 840 + 924 = 1764\)
Both methods give the same result: the compound interest is Rs. 1764.
Revision Table: Interest Formulas
| Concept | Formula |
|---|---|
| Simple Interest (SI) | \(SI = \frac{P \times R \times T}{100}\) |
| Amount (Simple Interest) | \(A = P + SI\) |
| Amount (Compound Interest) | \(A = P\left(1 + \frac{R}{100}\right)^n\) |
| Compound Interest (CI) | \(CI = A - P\) or \(CI = P\left[\left(1 + \frac{R}{100}\right)^n - 1\right]\) |
Additional Information on Compound Interest
Compound interest differs from simple interest because simple interest is calculated only on the initial principal amount. Compound interest leads to faster growth of money because the interest earned in each period is added to the principal for the next period's calculation.
- The frequency of compounding can affect the total compound interest. If interest is compounded more frequently (e.g., half-yearly, quarterly, monthly), the total interest earned will be higher, assuming the same annual rate.
- The power of compounding becomes more significant over longer periods.
Important Questions from Simple and Compound Both
X took a loan of Rs.1400 with simple interest for as many years as the rate of interest. If he paid Rs.1210 as interest at the end of that period, what was the rate of interest?
The S.I. on a certain sum of money for 4 years at 4 percent per annum exceeds the C.I. on the same sum for 3 years at 5 percent per annum by Rs. 57. Find the approximate sum.
The simple and compound interest that can be earned in two years at the same rate on a certain sum is Rs. 1,000 and Rs. 1,040 respectively. What is the rate (percent per annum) of interest?
Compound interest on a certain sum of money for 2 years at a rate of 'r' per cent per annum (compounding annually) is Rs. 8385. Simple interest on the same sum at the same rate for 2 years is Rs 7800. What is the value of r?
The compound interest accrued on Rs. 18000 in two years is Rs. 2995.2. What will be the simple interest accrued at the same rate of interest for the same sum for three years?
