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DSC1630 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
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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 in 30 months with
interest compounded semi-annually. To find the yearly interest
rate:
1. Convert 30 months to years: 3012=2.5 years\frac{30}{12} =
2.5 \text{ years}1230=2.5 years
2. Use the compound interest formula: A=P(1+rn)ntA = P \
left(1 + \frac{r}{n}\right)^{nt}A=P(1+nr)nt
o AAA = final amount (R56,000)
, o PPP = principal amount (R40,000)
o rrr = annual interest rate (unknown)
o nnn = number of times interest is compounded per
year (2 for semi-annual)
o ttt = number of years (2.5)
Rearranging for rrr:
56000=40000(1+r2)2×2.556000 = 40000 \left(1 + \frac{r}{2}\
right)^{2 \times 2.5}56000=40000(1+2r)2×2.5
5600040000=(1+r2)5\frac{56000}{40000} = \left(1 + \frac{r}{2}\
right)^54000056000=(1+2r)5 1.4=(1+r2)51.4 = \left(1 + \frac{r}
{2}\right)^51.4=(1+2r)5
Taking the fifth root of both sides:
1+r2=1.415≈1.0741 + \frac{r}{2} = 1.4^{\frac{1}{5}} \approx
1.0741+2r=1.451≈1.074 r2=1.074−1≈0.074\frac{r}{2} = 1.074 - 1
\approx 0.0742r=1.074−1≈0.074 r≈0.148 or 14.8%r \approx
0.148 \text{ or } 14.8\%r≈0.148 or 14.8%
So the closest answer is d. 14.41%.
Question 2:
Bhongo received R32,412.87 after investing some money at a
continuous compounding rate of 10.15% per year. To find the
invested amount:
1. Use the continuous compounding formula: A=PertA =
Pe^{rt}A=Pert
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