Compound Interest Calculation for 8-Monthly Compounding
This problem requires calculating the compound interest (CI) on a given principal amount (P) at a specific annual interest rate (R) for a certain time period (T), with compounding occurring 8-monthly.
Identify Given Values
- Principal (P) = Rs. 12,500
- Annual Interest Rate (R) = 15% p.a.
- Time (T) = 2 years
- Compounding Frequency = 8-monthly
Adjust Rate and Time for Compounding Period
Since interest is compounded 8-monthly, we need to adjust the rate and time period accordingly.
- Number of compounding periods per year = $\frac{12 \text{ months}}{8 \text{ months}} = 1.5$
- Interest rate per 8-monthly period (R') = $\frac{\text{Annual Rate}}{\text{Periods per year}} = \frac{15\%}{1.5} = 10\%$
- Total number of compounding periods (n) = Time in years $\times$ Periods per year = $2 \times 1.5 = 3$
Calculate Amount using Compound Interest Formula
The formula for the amount (A) after n periods is:
$A = P \left(1 + \frac{R'}{100}\right)^n$Substitute the adjusted values:
$A = 12500 \left(1 + \frac{10}{100}\right)^3$ $A = 12500 \left(1 + 0.1\right)^3$ $A = 12500 (1.1)^3$ $A = 12500 \times 1.331$ $A = 16637.5$The total amount after 2 years is Rs. 16,637.5.
Calculate Compound Interest
The compound interest (CI) is the difference between the final amount and the principal amount:
$CI = A - P$ $CI = 16637.5 - 12500$ $CI = 4137.5$Therefore, the compound interest is Rs. 4137.5.
Similar Questions
- A certain amount increases to five times its initial value after 10 years of compounding interest. How many years will it take for it to grow to twenty-five times its original amount?
- A vendor lends 74,000 rupees at a rate of 12% compound interest per annum, compounded annually. Find the interest for the 3rd year.
- A sum of money invested at compound interest amounts to twice itself in 4 years. In how many years will it become 8 times itself?
- What is the compound interest on Rs. 8000 for 2 year at 10% per annum?
- The compound interest on a certain sum for 3 years at 20% per annum is ₹864. Find the simple interest on the same sum at the same rate and period.
- What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 10% p.a.?
A sum of money becomes three times itself in 3 years at compound interest.
What is the rate of interest?
- If the amount is Rs. 600 and the Principal is Rs. 450, which is compounded yearly for 1 year, calculate the rate of interest.
- A certain sum amounts to Rs. $1,600$ in two years and to Rs. $2,000$ in three years at compound interest when compounded annually. Find the rate of interest.
- What will be the amount to be paid at the end of 5 years on Rs. 4500 at 10% per annum compounded annually?
Important Questions from Compound Interest
The certain sum amounts to Rs. 9,982.50 in \(2\frac{1}{2}\) years at 12% p.a., interest compounded 10-monthly. The sum (in Rs.) is:
The difference between the simple interest and the compound interest compounded annually on a certain sum of money for 2 years at a rate of 8% per annum is Rs. 16.80. Find the principle amount.
If a sum of ₹ 2000 is lent at 10% p.a. compound interest, what is the interest for the second year?
A sum becomes 5 times of itself in 3 years. at compound interest (interest is compounded annually). In how many years. will the sum becomes 125 times of itself?
If the compound interest on a certain sum of money for two years at 9% p.a. is Rs. 3,762, then the sum is:
