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
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.470. If the rate of interest is 10% p.a. then find the amount invested? (In Rs.)
- Suresh lent a sum of money on compound interest in such a way that it amounted to three times in 4 years. For how much time should he invest his money so that he gets back an amount which is 9 times of the sum of money lent by him?
The compound interest on a certain sum for 3 years at 8% per annum is Rs. 1,94,784. What is the simple interest on the $\frac{9}{10}$ part of the sum for the same time but at a rate of interest per annum which is $1\frac{1}{2}$ time the rate of interest per annum as applicable for compound interest?
- There is 60% increase in an amount in 4 years at simple interest. What will be the compound interest on Rs.49500 after 2 years at the same rate of interest? (In Rs.)
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.205. If the rate of interest is 5% p.a. then find the amount invested? (In Rs.)
