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
What is the compound interest (in Rs.) at the rate of 10%, compounded annually, for 3 years on the principal which in 8 years at the rate of 12% per annum gives Rs. 4,800 as simple interest?
A certain sum amounts to Rs. 15,500 in 2 years at 12% p.a. simple interest. If the same sum is compounded half-yearly at 10% per annum for \(1 \frac{1}{2}\) years, what will be the amount received?
The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half-yearly and yearly, is Rs. 88.80. What is the simple interest on the same sum for \(1\frac{2}{3}\) years at the same rate?
A sum of Rs. 7500 amounts to Rs. 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in Rs.) on the same sum for the same time and the same rate is:
A certain sum amounts to Rs.291600 in 2 years and to Rs.314928 in 3 years on compound interest compounded annually. How much will be the simple interest (in Rs.) on Rs.40000 at the same rate for 2 years?
