QUESTION 2
Boitumelo invests an amount of R28 000 for a period of 7 years. For the first two
years the interest was p.a. compounded semi-annually. The interest was then
changed to p.a. compounded quarterly.
Determine the value of the investment after the 7 -year period.
2.2 Convert an interest rate of p.a. compounded quarterly to an annual effective
interest rate.
2.3 A lawnmower was traded in for R236 after 10 years. The depreciation was
calculated at p.a. on a straight-line basis.
Determine the cost of the lawnmower 10 years ago.

Ask by Lambert Pope. in South Africa

Jan 23,2025

Question

QUESTION 2
Boitumelo invests an amount of R28 000 for a period of 7 years. For the first two
years the interest was p.a. compounded semi-annually. The interest was then
changed to p.a. compounded quarterly.
Determine the value of the investment after the 7 -year period.
2.2 Convert an interest rate of p.a. compounded quarterly to an annual effective
interest rate.
2.3 A lawnmower was traded in for R236 after 10 years. The depreciation was
calculated at p.a. on a straight-line basis.
Determine the cost of the lawnmower 10 years ago.

Ask by Lambert Pope. in South Africa

Jan 23,2025

UpStudy AI · Accepted Answer

**Question 2.2**

*Convert an interest rate of $$ 10\% $$ p.a. compounded quarterly to an annual effective interest rate.*

To convert a nominal interest rate compounded multiple times per year to an **effective annual interest rate (EAR)**, you can use the following formula:

$$
\text{EAR} = \left(1 + \frac{r_{\text{nominal}}}{m}\right)^m - 1
$$

where:
- $$ r_{\text{nominal}} $$ is the nominal annual interest rate (in decimal form).
- $$ m $$ is the number of compounding periods per year.

**Given:**
- Nominal interest rate, $$ r_{\text{nominal}} = 10\% = 0.10 $$
- Compounded quarterly, so $$ m = 4 $$

**Calculation:**

$$
\text{EAR} = \left(1 + \frac{0.10}{4}\right)^4 - 1 = \left(1 + 0.025\right)^4 - 1
$$

First, calculate $$ 1.025^4 $$:

$$
1.025^2 = 1.050625
$$
$$
1.050625^2 = 1.10381289
$$

$$
\text{EAR} = 1.10381289 - 1 = 0.10381289 \text{ or } 10.38\%
$$

**Answer:**  
The annual effective interest rate is **10.38 %**.
The annual effective interest rate is **10.38 %**.

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