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Please provide solutions for the following loan problems: 1. Calculate the total repayment amount for borrowing R 3000 over 24 months. 2. Determine the ratio of monthly installments for R2000 over 12

Mathematics

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Answers

2 parts
a

R3600\text{R}3600

b

R211.11\text{R}211.11

Step-by-step solution

5 steps

Here are the solutions to the loan problems:

Calculate the total repayment amount for borrowing R 3000 when repaying it over 24 months.

Step 1: Identify the monthly instalment from the table.
For a loan amount of R 3000 over 24 months, the monthly instalment is R 230.

Step 2: Calculate the total repayment amount.
Total repayment = Monthly instalment ×\times Number of months

Total repayment=R230×24\text{Total repayment} = \text{R}230 \times 24 Total repayment=R5520\text{Total repayment} = \text{R}5520

The total repayment amount is R 5520.

R5520\boxed{\text{R}5520}

Determine the ratio in its simplest form, of A to B, the monthly instalment for borrowing R2 000.

Step 1: Identify the values for A and B from the table.
For a loan amount of R 2000:
A (12 months instalment) = R 285
B (24 months instalment) = R 190

Step 2: Write the ratio A to B.

Ratio A : B=285:190\text{Ratio A : B} = 285 : 190

Step 3: Simplify the ratio by dividing both numbers by their greatest common divisor.
Both numbers are divisible by 5:

285÷5=57285 \div 5 = 57 190÷5=38190 \div 5 = 38

The ratio becomes 57:3857 : 38.
Both numbers are divisible by 19:

57÷19=357 \div 19 = 3 38÷19=238 \div 19 = 2

The ratio in its simplest form is 3 : 2.

3:2\boxed{3 : 2}

A customer borrowed R4 000 and plans to pay it in equal monthly instalments for 3 years. The customer was charged 30% pa. simple interest.

Part a· 2 steps

Calculate the interest on the loan for 3 years.

  1. Identify the given values.

    Principal (PP) = R 4000
    Interest rate (ii) = 30% p.a. = 0.30
    Number of years (nn) = 3 years

  2. Use the simple interest formula I=P×i×nI = P \times i \times n.

    I=R4000×0.30×3I = \text{R}4000 \times 0.30 \times 3 I=R1200×3I = \text{R}1200 \times 3 I=R3600I = \text{R}3600

    The interest on the loan is R 3600.

    R3600\boxed{\text{R}3600}

Part b

R211.11\text{R}211.11

Hence, determine the monthly instalment (C) for the total amount that must be paid back.

  1. Calculate the total amount to be paid back.

    Total amount = Principal + Interest

    Total amount=R4000+R3600\text{Total amount} = \text{R}4000 + \text{R}3600 Total amount=R7600\text{Total amount} = \text{R}7600
  2. Calculate the total number of months for repayment.

    Number of months = Number of years ×\times 12 months/year

    Number of months=3×12=36 months\text{Number of months} = 3 \times 12 = 36\, \text{months}
  3. Calculate the monthly instalment (C).

    Monthly instalment (C) = Total amount / Number of months

    C=R760036C = \frac{\text{R}7600}{36} C≈R211.111...C \approx \text{R}211.111...

    Rounding to two decimal places for currency:

    C≈R211.11C \approx \text{R}211.11

    The monthly instalment (C) is approximately R 211.11.

    R211.11\boxed{\text{R}211.11}
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