Ram invested 45% of his salary in a scheme for 3 years which offers 10% per annum compound interest, compounded annually.
If he receives Rs5,958 as total interest, then find Ram's salary?
This questions was previously asked in
SSC MTS 14th July 2022 Shift-3
Rs45,000
Incorrect AnswerRs50,000
Incorrect AnswerRs36,000
Incorrect AnswerExplanation:
- Ram invested 45% of his salary at 10% compound interest over three years.
- The total interest received from this investment is Rs5,958.
- The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
- Here, interest is compounded annually (n = 1), so the formula simplifies, and we focus on interest gained.
- To find Ram's salary, we first need to calculate his initial investment (P) that resulted in Rs5,958 in interest.
- Let's denote Ram's salary as S. Thus, the investment P = 0.45 * S.
- Using the compound interest formula, 5,958 = P * [(1 + 0.10)^3 - 1].
- Calculate: [(1 + 0.10)^3 - 1] = [1.1^3 - 1] = [1.331 - 1] = 0.331.
- Now, 5,958 = 0.331 * (0.45 * S).
- Solving for S, 5,958 = 0.14895 * S, S = 5,958 / 0.14895 ˜ Rs40,000.
Option:4 - Rs40,000
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