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A cellphone costs R5,000 cash. It can be bought on a 24-month contract for R390 per month, which includes R100 for airtime. Calculate: 1.1 the monthly payment for the handset only. 1.2 the total amoun

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Answers

4 parts
1.1

R290\text{R}290

1.2

R6960\text{R}6960

1.3

R1960\text{R}1960

1.4

19.6%19.6\%

Step-by-step solution

10 steps

Here are the solutions to the finance questions:

Part 1.1· 2 steps

  1. Identify the total monthly payment and the portion allocated to airtime.

    Total monthly payment = R390
    Monthly airtime allocation = R100

  2. Subtract the airtime allocation from the total monthly payment to find the payment for the handset only.

    Monthly payment for handset only = Total monthly payment - Monthly airtime allocation

    =R390−R100= \text{R}390 - \text{R}100 =R290= \text{R}290

    The monthly payment for the handset only is R290\boxed{\text{R}290}.

Part 1.2

R6960\text{R}6960

  1. Use the monthly payment for the handset only (from 1.1) and the contract duration.

    Monthly payment for handset only = R290
    Contract duration = 24 months

  2. Multiply the monthly handset payment by the number of months.

    Total paid for handset only = Monthly payment for handset only ×\times Number of months

    =R290×24= \text{R}290 \times 24 =R6960= \text{R}6960

    The total amount paid for the handset only over 24 months is R6960\boxed{\text{R}6960}.

Part 1.3

R1960\text{R}1960

  1. Identify the cash price of the cellphone and the total amount paid for the handset over 24 months.

    Cash price of cellphone = R5 000
    Total paid for handset only (from 1.2) = R6960

  2. Subtract the cash price from the total amount paid for the handset to find the interest added.

    Interest added = Total paid for handset only - Cash price

    =R6960−R5000= \text{R}6960 - \text{R}5000 =R1960= \text{R}1960

    The interest added over the 24 months is R1960\boxed{\text{R}1960}.

Part 1.4

19.6%19.6\%

  1. Recall the simple interest formula and identify the known values.

    Simple interest formula: I=P⋅r⋅tI = P \cdot r \cdot t
    Where:
    II = Interest added = R1960 (from 1.3)
    PP = Principal (cash price) = R5000
    tt = Time in years = 24 months = 2412\frac{24}{12} years = 2 years
    rr = Annual simple interest rate (to be calculated)

  2. Rearrange the formula to solve for rr.

    r=IP⋅tr = \frac{I}{P \cdot t}

  3. Substitute the values and calculate the rate.

    r=R1960R5000×2r = \frac{\text{R}1960}{\text{R}5000 \times 2} r=R1960R10000r = \frac{\text{R}1960}{\text{R}10000} r=0.196r = 0.196

  4. Convert the decimal rate to a percentage.

    r=0.196×100%r = 0.196 \times 100\% r=19.6%r = 19.6\%

    The annual simple interest rate is 19.6%\boxed{19.6\%}.

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