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Calculate simple interest for 1 year and total amount after 2 years, and compound interest for 2 years.

Mathematics

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4 parts
2.1

R900\text{R}900

2.2

R16800\text{R}16800

3.1

R13800\text{R}13800

3.2

R13891.50\text{R}13891.50

Step-by-step solution

11 steps

Here are the solutions to Question 2 and Question 3.

Part 2

Part 2.1

R900\text{R}900

  1. Identify the principal amount, interest rate, and time.

    Principal (PP) = R15 000
    Annual simple interest rate (rr) = 6% = 0.06
    Time (tt) = 1 year

  2. Use the simple interest formula I=P⋅r⋅tI = P \cdot r \cdot t to calculate the interest added each year.

    I=R15000×0.06×1I = \text{R}15000 \times 0.06 \times 1 I=R900I = \text{R}900

    The interest that will be added each year is R900\boxed{\text{R}900}.

Part 2.2

R16800\text{R}16800

  1. Identify the principal amount, annual simple interest rate, and total time.

    Principal (PP) = R15 000
    Annual simple interest rate (rr) = 6% = 0.06
    Time (tt) = 2 years

  2. Use the simple interest formula for total amount A=P(1+r⋅t)A = P(1 + r \cdot t).

    A=R15000(1+0.06×2)A = \text{R}15000(1 + 0.06 \times 2) A=R15000(1+0.12)A = \text{R}15000(1 + 0.12) A=R15000(1.12)A = \text{R}15000(1.12) A=R16800A = \text{R}16800

    The amount available in his account after 2 years will be R16800\boxed{\text{R}16800}.

Part 2.3· 3 steps

  1. Calculate the amount with compound interest at 5% compounded annually for 2 years.

    Principal (PP) = R15 000
    Annual compound interest rate (ii) = 5% = 0.05
    Number of compounding periods (nn) = 2 years
    Use the compound interest formula A=P(1+i)nA = P(1 + i)^n.

    A=R15000(1+0.05)2A = \text{R}15000(1 + 0.05)^2 A=R15000(1.05)2A = \text{R}15000(1.05)^2 A=R15000(1.1025)A = \text{R}15000(1.1025) A=R16537.50A = \text{R}16537.50
  2. Compare this amount to the amount calculated in 2.2 (simple interest at 6% for 2 years).

    Amount with simple interest (6%) = R16 800
    Amount with compound interest (5%) = R16 537.50

  3. Justify or refute the manager's claim.

    Since R16 800 > R16 537.50, Thabo would have less money with the 5% compound interest deal.
    Therefore, the manager's claim is refuted. Thabo's current deal of 6% simple interest is better.

Part 3

Pinkie wants to invest R12 000 at an interest rate of 5% per annum for 3 years.

Part 3.1

R13800\text{R}13800

  1. Identify the principal amount, annual simple interest rate, and time.

    Principal (PP) = R12 000
    Annual simple interest rate (rr) = 5% = 0.05
    Time (tt) = 3 years

  2. Use the simple interest formula for total amount A=P(1+r⋅t)A = P(1 + r \cdot t).

    A=R12000(1+0.05×3)A = \text{R}12000(1 + 0.05 \times 3) A=R12000(1+0.15)A = \text{R}12000(1 + 0.15) A=R12000(1.15)A = \text{R}12000(1.15) A=R13800A = \text{R}13800

    If simple interest is added, Pinkie will have R13800\boxed{\text{R}13800} in her account.

Part 3.2

R13891.50\text{R}13891.50

  1. Identify the principal amount, annual compound interest rate, and number of compounding periods.

    Principal (PP) = R12 000
    Annual compound interest rate (ii) = 5% = 0.05
    Number of compounding periods (nn) = 3 years (compounded annually)

  2. Use the compound interest formula A=P(1+i)nA = P(1 + i)^n.

    A=R12000(1+0.05)3A = \text{R}12000(1 + 0.05)^3 A=R12000(1.05)3A = \text{R}12000(1.05)^3 A=R12000(1.157625)A = \text{R}12000(1.157625) A=R13891.50A = \text{R}13891.50

    If interest is compounded annually, Pinkie will have R13891.50\boxed{\text{R}13891.50} in her account.

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