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Tumi saves R800 per month for two years. She then invests this amount for 36 months at a simple interest rate of 12.5% p.a. Calculate the total interest earned.

Mathematics

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Answers

3 parts
1.1

R19 200\text{R}19\,200

1.2

R7 200\text{R}7\,200

1.3

R26 400\text{R}26\,400

Step-by-step solution

2 steps

Here are the calculations for Tumi's investment:

Step 1: Calculate the total amount Tumi has saved.
Tumi saved R800 per month for two years.
First, convert the time into months:

Number of months=2 years×12 months/year=24 months\text{Number of months} = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}

Now, calculate the total amount saved:

Total saved=Monthly saving×Number of months\text{Total saved} = \text{Monthly saving} \times \text{Number of months} Total saved=R800×24\text{Total saved} = \text{R}800 \times 24 Total saved=R19 200\text{Total saved} = \text{R}19\,200

Part 1.1· 1 step

Calculate the amount that Tumi will be able to invest in the bank.

The amount Tumi will invest is the total amount he has saved.

Principal amount (P)=R19 200\text{Principal amount } (P) = \text{R}19\,200

The amount Tumi will be able to invest is R19 200\boxed{\text{R}19\,200}.

  1. Determine the interest Tumi will earn.

    The investment is for 36 months at 12.5% p.a. simple interest.
    First, convert the time into years:

    Time (t)=36 months12 months/year=3 years\text{Time } (t) = \frac{36 \text{ months}}{12 \text{ months/year}} = 3 \text{ years}

    Convert the annual interest rate to a decimal:

    Interest rate (r)=12.5%=12.5100=0.125\text{Interest rate } (r) = 12.5\% = \frac{12.5}{100} = 0.125

    Use the simple interest formula I=P⋅r⋅tI = P \cdot r \cdot t:

    I=R19 200×0.125×3I = \text{R}19\,200 \times 0.125 \times 3 I=R2 400×3I = \text{R}2\,400 \times 3 I=R7 200I = \text{R}7\,200

Part 1.2

R7 200\text{R}7\,200

Determine the interest he will earn from the bank.

The interest Tumi will earn is R7 200\boxed{\text{R}7\,200}.

  1. Calculate the total amount Tumi will receive at the end of the investment period.

    The total amount received is the principal plus the interest earned.

    Total amount (A)=P+I\text{Total amount } (A) = P + I A=R19 200+R7 200A = \text{R}19\,200 + \text{R}7\,200 A=R26 400A = \text{R}26\,400

Part 1.3

R26 400\text{R}26\,400

What is the total amount that he will receive at the end of the investment period?

The total amount Tumi will receive is R26 400\boxed{\text{R}26\,400}.

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