Question
Download Solution PDFA certain sum amounts to Rs. 7,200 in 2 years at 6% per annum compound interest, compounded annually. Find the sum (in Rs., to the nearest integer).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFData:
Amount after 2 years (A) = ₹7200
Annual interest rate (r) = 6%
Time (t) = 2 years
Concept:
For compound interest compounded annually,
A = P(1 + r/100)t. We can rearrange this to solve for P.
Solution:
Convert the annual interest rate from a percentage to a decimal
⇒ r = 6/100 = 0.06
The problem states that the interest is compounded annually, so n = 1
Substitute A, r, n, and t into the compound interest formula and solve for P
⇒ 7200 = P(1 + 0.06/1)(1×2)
⇒ 7200 = P(1 + 0.06)2
⇒ 7200 = P(1.06)2
⇒ 7200 = P(1.1236)
Solve for P
⇒ P = 7200 / 1.1236
⇒ P = 6408.35
Therefore, the initial sum (rounded to the nearest integer) is Rs. 6408.
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