STION 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 the
changed to p.a. compounded quarterly.
Determine the value of the investment after the 7-year period.

Question

STION 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 the
changed to

p.a. compounded quarterly.
Determine the value of the investment after the 7-year period.

UpStudy AI · Accepted Answer

To determine the value of Boitumelo's investment after 7 years with varying interest rates and compounding frequencies, we'll break the calculation into two distinct periods:

1. **First 2 Years:**
   - **Initial Investment (P):** R28,000
   - **Annual Interest Rate (r):** 12% (0.12)
   - **Compounding Frequency (n):** Semi-annually (2 times a year)
   - **Time (t):** 2 years

2. **Next 5 Years:**
   - **Interest Rate (r):** 10% (0.10)
   - **Compounding Frequency (n):** Quarterly (4 times a year)
   - **Time (t):** 5 years

### **Step 1: Calculate the Amount After the First 2 Years**

Using the compound interest formula:
$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

Plugging in the values:
$$
A_1 = 28,000 \left(1 + \frac{0.12}{2}\right)^{2 \times 2} = 28,000 \times (1.06)^4
$$

Calculating $$(1.06)^4$$:
$$
1.06^4 \approx 1.2625
$$

So,
$$
A_1 \approx 28,000 \times 1.2625 = 35,349 \text{ R}
$$

### **Step 2: Calculate the Amount After the Next 5 Years**

Now, $$A_1$$ becomes the principal for the next period.

$$
A_2 = 35,349 \left(1 + \frac{0.10}{4}\right)^{4 \times 5} = 35,349 \times (1.025)^{20}
$$

Calculating $$(1.025)^{20}$$:
$$
(1.025)^{20} \approx 1.6386
$$

So,
$$
A_2 \approx 35,349 \times 1.6386 \approx 57,924 \text{ R}
$$

### **Final Value of the Investment**

After 7 years, Boitumelo's investment grows to approximately **R57,924**.

---

**Summary:**
- **Initial Investment:** R28,000
- **After 2 Years:** R35,349
- **After 7 Years:** R57,924
After 7 years, Boitumelo's investment grows to approximately R57,924.

STION 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 the
changed to p.a. compounded quarterly.
Determine the value of the investment after the 7-year period.

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Solución

The Deep Dive

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STION 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 the changed to p.a. compounded quarterly. Determine the value of the investment after the 7-year period.

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Responder

Solución

The Deep Dive

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Latest Economics Questions

STION 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 the
changed to p.a. compounded quarterly.
Determine the value of the investment after the 7-year period.