Question
Download Solution PDFThe simple interest accrued on a sum of certain principal is Rs. 2,000 in five years at the rate of 4 p.c.p.a. What would be the compound interest accrued on same principa years?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simple Interest (SI) = ₹2000
Rate of interest (r) = 4% per annum
Time (t) = 5 years
Formula Used:
Simple Interest (SI) = (Principal (P) × Rate (r) × Time (t)) / 100
Compound Interest (CI) = Amount (A) - Principal (P)
Amount (A) = P\((1 + \frac{r}{100})^n\), where n is the number of compounding periods.
Calculations:
Principal using the simple interest formula:
2000 = (P × 4 × 5) / 100
2000 = 20P / 100
2000 = P / 5
P = 2000 × 5 = ₹10000
Compound interest on the same principal (₹10000) at 4% per annum for 2 years.
First, calculate the Amount:
A = 10000\((1 + \frac{4}{100})^2\)
A = 10000\((1 + 0.04)^2\)
A = 10000(1.04)2
A = 10000 × 1.0816
A = ₹10816
CI = A - P
CI = ₹10816 - ₹10000
CI = ₹816
∴ The compound interest earned on the same sum at the same rate for two years is ₹816.
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