DSC1630
Assignment 1
DUE 8
August 2024
[Type the abstract of the document here. The abstract is typically a short summary of the
contents of the document. Type the abstract of the document here. The abstract is typically a
short summary of the contents of the document.]
[Pick the date]
,
Book
Introduction to Financial Mathematics
DSC1630 Assignment 1 (COMPLETE ANSWERS) Semester 2 2024
(234521)- DUE 8 August 2024 ; 100% TRUSTED Complete, trusted solutions
and explanations
Question 1 Not yet answered Marked out of 1.00 QUIZ You have invested R1
500 in an account earning 6,57% simple interest. The balance in the account
16 months later is a. R1 636,94. b. R2 814,00. c. R1 631,40. d. R1 644,02.
Clear my choice DSC1630-24-S2 Welcome Message Assessment 1
To find the balance in the account after 16 months with simple interest, we can use the formula:
A=P×(1+rt)A = P \times (1 + rt)A=P×(1+rt)
Where:
AAA is the amount (final balance)
PPP is the principal amount (initial investment)
rrr is the annual interest rate (as a decimal)
ttt is the time in years
Let's calculate it:
P=R1,500P = R1,500P=R1,500
r=6.57%=0.0657r = 6.57\% = 0.0657r=6.57%=0.0657
t=1612 yearst = \frac{16}{12} \text{ years}t=1216 years
Now, calculate the balance AAA:
A=1500×(1+0.0657×1612)A = 1500 \times (1 + 0.0657 \times \frac{16}
{12})A=1500×(1+0.0657×1216)
A=1500×(1+0.0657×1.3333)A = 1500 \times (1 + 0.0657 \times
1.3333)A=1500×(1+0.0657×1.3333)
A=1500×(1+0.0876)A = 1500 \times (1 + 0.0876)A=1500×(1+0.0876)
A=1500×1.0876A = 1500 \times 1.0876A=1500×1.0876
, A≈R1,631.40A \approx R1,631.40A≈R1,631.40
The correct answer is c. R1,631.40.
Question 2 Not yet answered Marked out of 1.00 QUIZ If money is worth 12%
per annum compounded monthly, how long will it take the principal P
tobecome four times the original value? a. 11,61 years b. 7,27 years c. 69,66
years d. 139,32 years Clear my choice DSC1630-24-S2 Welcome Message
Assessment 1
To find how long it will take for an investment to become four times its original value with
compound interest, we use the compound interest formula:
A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}A=P(1+nr)nt
Where:
AAA is the final amount
PPP is the principal (initial amount)
rrr is the annual interest rate (as a decimal)
nnn is the number of times the interest is compounded per year
ttt is the number of years
Given:
A=4PA = 4PA=4P (because the amount becomes four times the principal)
r=12%=0.12r = 12\% = 0.12r=12%=0.12
n=12n = 12n=12 (compounded monthly)
We need to find ttt.
Substitute the values into the formula:
4P=P(1+0.1212)12t4P = P\left(1 + \frac{0.12}{12}\right)^{12t}4P=P(1+120.12)12t
Divide both sides by PPP:
4=(1+0.1212)12t4 = \left(1 + \frac{0.12}{12}\right)^{12t}4=(1+120.12)12t
Calculate 1+0.12121 + \frac{0.12}{12}1+120.12:
