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SC1630 Assignment 2 (COMPLETE ANSWERS) Semester 2 2024 (234642) - DUE 22 August 2024
SC1630 Assignment 2 (COMPLETE ANSWERS) Semester 2 2024 (234642) - DUE 22 August 2024
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,DSC1630 Assignment 2 (COMPLETE ANSWERS)Semester 2 2024 (234642) - DUE 22 August
2024 ; 100% TRUSTED Complete, trusted
solutions and explanations.
Question 1 Complete Mark 1.00 out of 1.00 Question 2
Complete Mark 1.00 out of 1.00 QUIZ Mary invested R40 000 in
order to have R56 000 available in 30 months’ time. The yearly
rate, compounded semi-annually, is a. 7,21%. b. 8,00%. c.
13,92%. d. 14,41%. Bhongo received R32 412,87 after investing
an amount of money in an account earning interest at a
continuous compounding rate of 10,15%per year. The amount
of money that he invested 57 weeks earlier, is approximately a.
R29 000,00. b. R29 153,86. c. R32 768,16. d. R36 227,38.
Question 3 Complete Mark 1.00 out of 1.00 Question 4
Complete Mark 1.00 out of 1.00
Question 1
Mary invested R40,000 to have R56,000 available in 30 months'
time. We need to find the yearly rate, compounded semi-
annually.
The formula for compound interest is:
A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}A=P(1+nr)nt
Where:
A=56,000A = 56,000A=56,000
P=40,000P = 40,000P=40,000
, rrr is the annual interest rate
n=2n = 2n=2 (compounded semi-annually)
t=3012=2.5t = \frac{30}{12} = 2.5t=1230=2.5 years
Substitute the values:
56,000=40,000(1+r2)2⋅2.556,000 = 40,000 \left(1 + \frac{r}{2}\
right)^{2 \cdot 2.5}56,000=40,000(1+2r)2⋅2.5
Simplify and solve for rrr:
1.4=(1+r2)51.4 = \left(1 + \frac{r}{2}\right)^51.4=(1+2r)5
Take the fifth root of both sides:
1+r2=(1.4)1/51 + \frac{r}{2} = (1.4)^{1/5}1+2r=(1.4)1/5
Calculate:
1+r2≈1.0691 + \frac{r}{2} \approx 1.0691+2r≈1.069
Subtract 1 from both sides:
r2≈0.069\frac{r}{2} \approx 0.0692r≈0.069
Multiply both sides by 2:
r≈0.138r \approx 0.138r≈0.138
Convert to a percentage:
r≈13.8%r \approx 13.8\%r≈13.8%
The closest answer is:
c.13,92%c. 13,92\%c.13,92%
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