Question
Download Solution PDFThe difference between the amounts of compound interest and simple interest received on the same sum in two years is Rs 40. If the interest rate is 4% per annum, then calculate the amount invested (in Rs)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The difference between the amounts of compound interest and simple interest received on the same sum in two years is Rs 40.
Interest rate = 4% per annum
Formula Used:
Compound Interest for 2 years: A = P(1 + (r)/(100))2
Simple Interest for 2 years: SI = (P × r × t)/(100)
Difference between CI and SI for 2 years: CI - SI
Calculation:
Let the principal amount be P Rs.
Simple Interest for 2 years:
SI = (P × 4 × 2)/(100)
SI = (8P)/(100)
SI = 0.08P
Compound Interest for 2 years:
A = P(1 + (4)/(100))2
A = P(1 + 0.04)2
A = P(1.04)2
A = P × 1.0816
CI = A - P
CI = P × 1.0816 - P
CI = P(1.0816 - 1)
CI = P × 0.0816
Difference between CI and SI:
CI - SI = P × 0.0816 - 0.08P
CI - SI = 0.0816P - 0.08P
CI - SI = 0.0016P
Given difference is Rs 40:
⇒ 0.0016P = 40
⇒ P = (40)/(0.0016)
⇒ P = 25000
The amount invested is Rs 25000.
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