Question
Download Solution PDFA sum of money invested at simple interest in a bank amounts to Rs.944 in a period of 3 years, while it amounts to Rs.1,136 in a period of 7 years. What is the rate of interest?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Amount (A1) after 3 years = ₹944
Amount (A2) after 7 years = ₹1136
Formula Used:
Amount (A) = Principal (P) + Simple Interest (SI)
Simple Interest (SI) = (P × R × T) / 100
Where P is the principal, R is the rate of interest, and T is the time period.
Calculation:
Let the principal be P and the rate of interest be R% per annum.
According to the given information:
P + (P × R × 3) / 100 = 944 (Equation 1)
P + (P × R × 7) / 100 = 1136 (Equation 2)
Subtracting Equation 1 from Equation 2:
[P + (P × R × 7) / 100] - [P + (P × R × 3) / 100] = 1136 - 944
⇒ (7PR / 100) - (3PR / 100) = 192
⇒ 4PR / 100 = 192
⇒ PR / 25 = 192
⇒ PR = 192 × 25
⇒ PR = 4800 (Equation 3)
Substitute the value of PR from Equation 3 into Equation 1:
P + (4800 × 3) / 100 = 944
⇒ P + 144 = 944
⇒ P = 944 - 144
⇒ P = 800
Now substitute the value of P in Equation 3:
800 × R = 4800
⇒ R = 4800 / 800
⇒ R = 6
∴ The rate of interest is 6% per annum.
Last updated on Dec 9, 2024
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