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DSC1630 Assignment 3 (COMPLETE ANSWERS) Semester 2 2024 (234683) - DUE 5 September 2024
DSC1630 Assignment 3 (COMPLETE ANSWERS) Semester 2 2024 (234683) - DUE 5 September 2024
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,DSC1630 Assignment 3 (COMPLETE ANSWERS)Semester 2 2024 (234683) - DUE 5 September
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 Quarterly payments of R7
000 are made into an account earning 6,57% per year,
compounded monthly. The accumulated amount after 12
yearsis a. R122 095,12. b. R336 000,00. c. R231 205,73. d. R506
569,30. Cyril buys a house and makes a down payment of 35%
of the price of the house. He manages to secure a loan at an
interest rate of 13,25% peryear, compounded monthly, for a
period of 20 years. His monthly payment is R10 437,26. The size
of the down payment (to the nearest rand) is a. R527 959. b.
R472 500. c. R307 125. d. R876 730.
1. Accumulated Amount with Quarterly Payments:
Quarterly payments of R7,000 are made into an account
earning 6.57% per year, compounded monthly. We need to find
the accumulated amount after 12 years.
Convert annual interest rate to monthly:
o Monthly interest rate: 6.57%12=0.5475%=0.005475\
frac{6.57\%}{12} = 0.5475\% = 0.005475126.57%
=0.5475%=0.005475
Future Value of an Annuity Formula:
, o Quarterly deposit: R7,000
o Monthly compounding interest rate: 0.005475
o Number of quarters: 12×4=4812 \times 4 =
4812×4=48 quarters
The future value of the annuity can be calculated using:
FV=P[(1+i)n−1i]FV = P \left[\frac{(1 + i)^n - 1}{i}\
right]FV=P[i(1+i)n−1]
where P=7000P = 7000P=7000, i=0.005475i =
0.005475i=0.005475, and n=48n = 48n=48:
FV=7000[(1+0.005475)48−10.005475]FV = 7000 \left[\frac{(1 +
0.005475)^{48} - 1}{0.005475}\
right]FV=7000[0.005475(1+0.005475)48−1]
FV=7000[(1.005475)48−10.005475]FV = 7000 \left[\
frac{(1.005475)^{48} - 1}{0.005475}\
right]FV=7000[0.005475(1.005475)48−1]
FV≈7000[1.346569−10.005475]FV \approx 7000 \left[\
frac{1.346569 - 1}{0.005475}\
right]FV≈7000[0.0054751.346569−1]
FV≈7000×63.293≈442,051.13FV \approx 7000 \times 63.293 \
approx 442,051.13FV≈7000×63.293≈442,051.13
The closest answer is d. R506,569.30.
2. Size of the Down Payment:
Cyril buys a house and makes a down payment of 35% of the
house price. He secures a loan with an interest rate of 13.25%
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