If the simple interest on a certain sum for 1.5 years at 8% p.a is Rs 360.…
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If the simple interest on a certain sum for 1.5 years at 8% p.a is Rs 360. Find the compound interest on the same sum for the same rate of interest but double the time ?
Answer: C. Rs 779.13 — Step-by-Step SolutionTo find the compound interest, we first need to determine the principal amount using the simple interest information provided. Calculate…
- A.
Rs 778
- B.
Rs 778.13
- C.
Rs 779.13
- D.
Rs 777.13
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Correct answer: C
Step-by-Step Solution
To find the compound interest, we first need to determine the principal amount using the simple interest information provided.
Calculate the Principal (P):
Formula: SI = (P * r * t) / 100
Given: SI = 360, r = 8%, t = 1.5 years
360 = (P * 8 * 1.5) / 100
360 = (P * 12) / 100
360 * 100 = 12 * P
36,000 = 12 * P
P = 3,000
Calculate Compound Interest (CI):
Time is doubled: t = 1.5 years * 2 = 3 years.
Rate: r = 8%
Formula for Amount (A) with CI: A = P * (1 + r/100)^t
A = 3000 * (1 + 8/100)^3
A = 3000 * (1.08)^3
A = 3000 * 1.259712
A = 3,779.136
Find the Interest:
CI = Amount - Principal
CI = 3,779.136 - 3,000
CI = 779.136 (approximately Rs. 779.13)