To find the rate percent per annum at which Rs 2,000 will amount to Rs 2,315.25 in 3 years using the compound interest formula, we can follow these steps:
1. Identify the Given Values: - Principal (P) = Rs 2,000 - Amount (A) = Rs 2,315.25 - Time (T) = 3 years
2. Use the Compound Interest Formula: The formula for compound interest is: A=P(1+r100)t where: - A = Amount - P = Principal - r = Rate of interest per annum - t = Time in years
3. Substitute the Known Values into the Formula: 2315.25=2000(1+r100)3
4. Divide Both Sides by 2000: 2315.252000=(1+r100)3 1.157625=(1+r100)3
5. Take the Cube Root of Both Sides: √(3)1.157625=1+r100 Calculating the cube root: 1.05=1+r100
To calculate the interest rate per annum, you need to divide the amount of interest paid by the principal amount borrowed or invested, and then multiply by the number of periods in a year.
r = [(A/P)(1/t)] - 1, where 'r' is the annual interest rate, 'A' is the amount after 't' years, 'P' is the principal amount, and 't' is the time in years. Therefore, the annual interest rate that will grow an initial amount of ₹2,000 to ₹2,205 in 2 years, when calculated annually, is approximately 5%.
The equation for calculating interest rates is as follows: Interest = P x R x N. Where P equals the principal amount (the beginning balance), and R stands for the interest rate (usually per year, expressed as a decimal). Finally, N corresponds to the number of time periods (generally one-year time periods).
APR = (((Interest charges + fees) ÷ Loan amount) ÷ Number of days in loan term x 365) x 100. This formula is a lot to digest and can help you understand how APR is calculated. Fortunately, the Truth in Lending Act requires lenders to disclose APR when they offer you credit.
Find the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at the rate of 5% per annum gives Rs 1200 as simple interest. ∴ The required compound interest is Rs.1,261.
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