Question
Question 26
Mr. B has been given an opportunity to receive R 20 000 six years from now and another R 30 000 seven years from now. If he can earn 10% p.a. on this investment, where interest is compounded quarterly, what amount must he invest today to pay for this opportunity?
R 693.33
R 3 964.11
R 5 795.41
R 6 551.72
R 26 083.84
1 points
Question 27
A principal of R1 700.00 is invested for 2.5 years at a rate of 6.5% per annum compounded quarterly. Determine what the investment will amount to at the end of the term and how much interest will be earned.
R1997.35
R1769.91
R3191.13
R1989.86
None of the above
Mr. B has been given an opportunity to receive R 20 000 six years from now and another R 30 000 seven years from now. If he can earn 10% p.a. on this investment, where interest is compounded quarterly, what amount must he invest today to pay for this opportunity?
R 693.33
R 3 964.11
R 5 795.41
R 6 551.72
R 26 083.84
1 points
Question 27
A principal of R1 700.00 is invested for 2.5 years at a rate of 6.5% per annum compounded quarterly. Determine what the investment will amount to at the end of the term and how much interest will be earned.
R1997.35
R1769.91
R3191.13
R1989.86
None of the above
Answers
GPT-4o mini
To solve these problems, we need to use the formulas for present value (PV) and future value (FV) of an investment compounded quarterly.
### Question 26
**Future Value of Cash Flows:**
Mr. B has two cash inflows:
1. R20,000 in 6 years
2. R30,000 in 7 years
**Interest rate (i):** 10% p.a. compounded quarterly means \( r = \frac{0.10}{4} = 0.025 \) per quarter.
**Time (n):**
- In 6 years, there are \( 6 \times 4 = 24 \) quarters.
- In 7 years, there are \( 7 \times 4 = 28 \) quarters.
**Present Value Calculation:**
1. Present Value of R20,000 received in 6 years:
\[
PV_1 = \frac{20000}{(1 + 0.025)^{24}} = \frac{20000}{(1.025)^{24}} \approx \frac{20000}{1.7137} \approx 11673.05
\]
2. Present Value of R30,000 received in 7 years:
\[
PV_2 = \frac{30000}{(1 + 0.025)^{28}} = \frac{30000}{(1.025)^{28}} \approx \frac{30000}{1.8509} \approx 16212.43
\]
**Total Present Value:**
\[
PV_{total} = PV_1 + PV_2 \approx 11673.05 + 16212.43 \approx 27885.48
\]
This amount represents how much Mr. B must invest today to cover these cash flows.
### Question 27
To calculate the future value of the R1,700 investment compounded quarterly at a rate of 6.5% over 2.5 years, we follow these steps:
**Principal (P):** R1,700
**Interest rate (i):** 6.5% p.a. compounded quarterly means \( r = \frac{0.065}{4} = 0.01625 \) per quarter.
**Time (n):** 2.5 years means \( 2.5 \times 4 = 10 \) quarters.
**Future Value Calculation:**
\[
FV = P \times (1 + r)^n = 1700 \times (1 + 0.01625)^{10} = 1700 \times (1.01625)^{10}
\]
Calculating \( (1.01625)^{10} \):
\[
(1.01625)^{10} \approx 1.1717
\]
Now,
\[
FV \approx 1700 \times 1.1717 \approx 1992.89
\]
Now, to calculate how much interest was earned:
\[
\text{Interest} = FV - P = 1992.89 - 1700 \approx 292.89
\]
None of the answers given match exactly, so for Question 27, the correct answer is **None of the above**.
To summarize:
- **Question 26 Present Value Required:** R 27885.48 (no option matches).
- **Question 27 Future Value:** R 1992.89 (None of the above matches the options given).
### Question 26
**Future Value of Cash Flows:**
Mr. B has two cash inflows:
1. R20,000 in 6 years
2. R30,000 in 7 years
**Interest rate (i):** 10% p.a. compounded quarterly means \( r = \frac{0.10}{4} = 0.025 \) per quarter.
**Time (n):**
- In 6 years, there are \( 6 \times 4 = 24 \) quarters.
- In 7 years, there are \( 7 \times 4 = 28 \) quarters.
**Present Value Calculation:**
1. Present Value of R20,000 received in 6 years:
\[
PV_1 = \frac{20000}{(1 + 0.025)^{24}} = \frac{20000}{(1.025)^{24}} \approx \frac{20000}{1.7137} \approx 11673.05
\]
2. Present Value of R30,000 received in 7 years:
\[
PV_2 = \frac{30000}{(1 + 0.025)^{28}} = \frac{30000}{(1.025)^{28}} \approx \frac{30000}{1.8509} \approx 16212.43
\]
**Total Present Value:**
\[
PV_{total} = PV_1 + PV_2 \approx 11673.05 + 16212.43 \approx 27885.48
\]
This amount represents how much Mr. B must invest today to cover these cash flows.
### Question 27
To calculate the future value of the R1,700 investment compounded quarterly at a rate of 6.5% over 2.5 years, we follow these steps:
**Principal (P):** R1,700
**Interest rate (i):** 6.5% p.a. compounded quarterly means \( r = \frac{0.065}{4} = 0.01625 \) per quarter.
**Time (n):** 2.5 years means \( 2.5 \times 4 = 10 \) quarters.
**Future Value Calculation:**
\[
FV = P \times (1 + r)^n = 1700 \times (1 + 0.01625)^{10} = 1700 \times (1.01625)^{10}
\]
Calculating \( (1.01625)^{10} \):
\[
(1.01625)^{10} \approx 1.1717
\]
Now,
\[
FV \approx 1700 \times 1.1717 \approx 1992.89
\]
Now, to calculate how much interest was earned:
\[
\text{Interest} = FV - P = 1992.89 - 1700 \approx 292.89
\]
None of the answers given match exactly, so for Question 27, the correct answer is **None of the above**.
To summarize:
- **Question 26 Present Value Required:** R 27885.48 (no option matches).
- **Question 27 Future Value:** R 1992.89 (None of the above matches the options given).