Loans and Investments Activity 3

1.1 Tumi started saving R800 per month two years ago so that he can take this money and invest it with a bank to put down a deposit when buying a house.

Tumi approached a bank that offered him [tex]12.5\%[/tex] p.a. simple interest for a period of 36 months on the total amount saved.

1.1.1 Calculate how much Tumi would be able to invest with the bank if he invests the entire amount.
(3)

1.1.2 Calculate the interest earned in this period.
(4)

1.1.3 What is the total amount that he will receive at the end of the investment period?
(2)



Answer :

Certainly! Let's break down the solution step-by-step for each sub-question.

### 1.1.1 Calculate how much Tumi would be able to invest with the bank, if he invests the entire amount.
Tumi starts saving R800 per month for 2 years (24 months).

1. Determine the total savings over the period:

[tex]\[ \text{Total Savings} = \text{Monthly Savings} \times \text{Number of Months} \][/tex]
[tex]\[ \text{Total Savings} = 800 \, \text{R/month} \times 24 \, \text{months} \][/tex]

Result:
[tex]\[ \text{Total Savings} = 19,200 \, \text{R} \][/tex]

So, Tumi would be able to invest R19,200 with the bank.


### 1.1.2 Calculate the interest earned in this period.
The bank offers an annual simple interest rate of [tex]\(12.5\%\)[/tex] over a period of 36 months (3 years).

1. Convert the percentage to a decimal:

[tex]\[ \text{Interest Rate} = \frac{12.5}{100} = 0.125 \][/tex]

2. Convert months to years for the investment period:

[tex]\[ \text{Investment Period (Years)} = \frac{36 \, \text{months}}{12 \, \text{months/year}} = 3 \, \text{years} \][/tex]

3. Calculate the interest earned using the formula for simple interest:

[tex]\[ \text{Interest Earned} = \text{Principal} \times \text{Interest Rate} \times \text{Time (Years)} \][/tex]
[tex]\[ \text{Interest Earned} = 19,200 \, \text{R} \times 0.125 \times 3 \, \text{years} \][/tex]

Result:
[tex]\[ \text{Interest Earned} = 7,200 \, \text{R} \][/tex]

So, the interest earned in this period is R7,200.


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

1. Calculate the total amount received:

[tex]\[ \text{Total Amount Received} = \text{Principal} + \text{Interest Earned} \][/tex]
[tex]\[ \text{Total Amount Received} = 19,200 \, \text{R} + 7,200 \, \text{R} \][/tex]

Result:
[tex]\[ \text{Total Amount Received} = 26,400 \, \text{R} \][/tex]

So, the total amount that Tumi will receive at the end of the investment period is R26,400.


### Summary:
1. Amount Tumi will invest: R19,200
2. Interest earned in 36 months: R7,200
3. Total amount received at the end of the investment period: R26,400