A person invested a certain amount of money at 10% annual interest, compounded…
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A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is ?
- A.
16000
- B.
15000
- C.
13000
- D.
15000
Attempted by 34 students.
Show answer & explanation
Correct answer: A
Key idea: convert the annual interest rate to a half-year rate and use the number of half-year periods.
Let P be the principal. The half-year interest rate = 10% ÷ 2 = 5% = 0.05. Number of half-year periods in 1.5 years = 1.5 × 2 = 3.
Write the amount equation: P × (1.05)^3 = 18522. So P = 18522 ÷ (1.05)^3.
Compute (1.05)^3 = 1.05 × 1.05 × 1.05 = 1.157625.
Therefore P = 18522 ÷ 1.157625 = 16000.
Hence the invested amount is Rs 16000.