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A boy's parents gave him R30 000 for his 21st birthday. His parents said that they had invested a sum of money on his 10th birthday that had grown at 13,5% p.a. CI for 11 years. How much was invested 11 years ago?

Mathematics

ScanSolve AI Answer

Answer

R7 200.00\text{R}7\,200.00

Step-by-step solution

4 steps
  1. Identify the given values and the compound interest formula.

    The future value (AA) is R30 000.
    The annual interest rate (ii) is 13.5% or 0.135.
    The number of years (nn) is 11.
    We need to find the principal amount (PP) that was invested.
    The compound interest formula is:

    A=P(1+i)nA = P(1 + i)^n
  2. Substitute the given values into the formula.

    30 000=P(1+0.135)1130\,000 = P(1 + 0.135)^{11}
  3. Calculate the term (1+0.135)11(1 + 0.135)^{11}.

    30 000=P(1.135)1130\,000 = P(1.135)^{11} 30 000=P(4.168716...)30\,000 = P(4.168716...)
  4. Solve for PP.

    P=30 0004.168716...P = \frac{30\,000}{4.168716...} P≈7200.00P \approx 7200.00

    The amount invested 11 years ago was R7 200.00.

    R7 200.00\text{R}7\,200.00
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