,DSC1630 Assignment 4 (COMPLETE ANSWERS)
Semester 1 2025 (239973) - DUE 8 May 2025;
100% TRUSTED Complete, trusted solutions and
explanations.
MULTIPLE CHOICE,ASSURED EXCELLENCE
Question 1 An interest rate of 17,5% per year, compounded
quarterly, is equivalent to a continuous compounding rate of [1]
17,128%. [2] 17,185%. [3] 17,500%. [4] 17,888%. [5] 19,125%.
Question 2 An amount borrowed at 29% interest per year,
compounded continuously, has accumulated to R38 279,20
after four years. The initial amount borrowed was [1] R7 160,73.
[2] R12 000,00. [3] R12 005,53. [4] R13 823,05. [5] R17 721,85.
20 2.2. COMPULSORY ASSIGNMENT 02 DSC1630/101 Question
3 The effective rate for a continuous compounding rate of
17,5% per year, is [1] 16,13%. [2] 17,50%. [3] 19,12%. [4]
19,13%. [5] 21,08%. Questions 4 and 5 relate to the following
situation: An amount of R10 000 was invested in a special
savings account on 15 May at an interest rate of 15% per
annum, compounded quarterly for seven months. Interest is
calculated on 1 January, 1 April, 1 July and 1 October of every
year. Question 4 If simple interest is used for the odd periods
and compound interest for the rest of the term, the amount of
interest received after seven months is [1] R665,54. [2] R896,95.
[3] R901,35. [4] R1 644,57. [5] none of the above. Question 5 If
fractional compounding is used for the full term of seven
, months, the total amount of interest received is [1] R892,79. [2]
R894,04. [3] R898,43. [4] R901,73. [5] none of the above. 21
Question 1: Equivalent Continuous Compounding Rate
We use the formula to convert a nominal rate rrr (compounded
quarterly) to a continuously compounded rate rcr_crc:
rc=mln(1+rm)r_c = m \ln \left( 1 + \frac{r}{m} \right)rc
=mln(1+mr)
where:
r=17.5%=0.175r = 17.5\% = 0.175r=17.5%=0.175 (nominal
annual rate)
m=4m = 4m=4 (since it's compounded quarterly)
rc=4ln(1+0.1754)r_c = 4 \ln \left( 1 + \frac{0.175}{4} \right)rc
=4ln(1+40.175)rc=4ln(1.04375)r_c = 4 \ln (1.04375)rc
=4ln(1.04375)rc≈4×0.04211r_c \approx 4 \times 0.04211rc
≈4×0.04211r_c \approx 0.1684 \text{ (or 16.84%)}
None of the given options match exactly, but the closest option
is [2] 17.185%.
Question 2: Initial Amount for Continuous Compounding
The formula for continuous compounding is:
A=PertA = P e^{rt}A=Pert
where:
Semester 1 2025 (239973) - DUE 8 May 2025;
100% TRUSTED Complete, trusted solutions and
explanations.
MULTIPLE CHOICE,ASSURED EXCELLENCE
Question 1 An interest rate of 17,5% per year, compounded
quarterly, is equivalent to a continuous compounding rate of [1]
17,128%. [2] 17,185%. [3] 17,500%. [4] 17,888%. [5] 19,125%.
Question 2 An amount borrowed at 29% interest per year,
compounded continuously, has accumulated to R38 279,20
after four years. The initial amount borrowed was [1] R7 160,73.
[2] R12 000,00. [3] R12 005,53. [4] R13 823,05. [5] R17 721,85.
20 2.2. COMPULSORY ASSIGNMENT 02 DSC1630/101 Question
3 The effective rate for a continuous compounding rate of
17,5% per year, is [1] 16,13%. [2] 17,50%. [3] 19,12%. [4]
19,13%. [5] 21,08%. Questions 4 and 5 relate to the following
situation: An amount of R10 000 was invested in a special
savings account on 15 May at an interest rate of 15% per
annum, compounded quarterly for seven months. Interest is
calculated on 1 January, 1 April, 1 July and 1 October of every
year. Question 4 If simple interest is used for the odd periods
and compound interest for the rest of the term, the amount of
interest received after seven months is [1] R665,54. [2] R896,95.
[3] R901,35. [4] R1 644,57. [5] none of the above. Question 5 If
fractional compounding is used for the full term of seven
, months, the total amount of interest received is [1] R892,79. [2]
R894,04. [3] R898,43. [4] R901,73. [5] none of the above. 21
Question 1: Equivalent Continuous Compounding Rate
We use the formula to convert a nominal rate rrr (compounded
quarterly) to a continuously compounded rate rcr_crc:
rc=mln(1+rm)r_c = m \ln \left( 1 + \frac{r}{m} \right)rc
=mln(1+mr)
where:
r=17.5%=0.175r = 17.5\% = 0.175r=17.5%=0.175 (nominal
annual rate)
m=4m = 4m=4 (since it's compounded quarterly)
rc=4ln(1+0.1754)r_c = 4 \ln \left( 1 + \frac{0.175}{4} \right)rc
=4ln(1+40.175)rc=4ln(1.04375)r_c = 4 \ln (1.04375)rc
=4ln(1.04375)rc≈4×0.04211r_c \approx 4 \times 0.04211rc
≈4×0.04211r_c \approx 0.1684 \text{ (or 16.84%)}
None of the given options match exactly, but the closest option
is [2] 17.185%.
Question 2: Initial Amount for Continuous Compounding
The formula for continuous compounding is:
A=PertA = P e^{rt}A=Pert
where:
