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
Understanding the problem:
Principal amount (P) = R1 500
Interest rate (R) = 6.57% per year
Time (T) = 16 months
Formula for Simple Interest:
Simple Interest (SI) = (P * R * T) / 100
Calculations:
1. Convert months to years: 16 months = 16/12 = 4/3 years
2. Calculate Simple Interest: SI = (1500 * 6.57 * 4/3) / 100 = R131.40
3. Calculate the balance: Balance = Principal + Simple Interest = 1500 + 131.40 = R1631.40
Answer:
The balance in the account 16 months later is R1 631.40.
Therefore, the correct option 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 what amount of time it will require for a speculation to become
multiple times its unique worth with accumulate interest, we utilize the
self multiplying dividends recipe:
A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}A=P(1+nr)nt
Where:
• AAA is the last sum
• PPP is the head (beginning sum)
• rrr is the yearly loan cost (as a decimal)
• nnn is the times the interest is accumulated each year
• ttt is the quantity of years
Given:
• A=4PA = 4PA=4P (in light of the fact that the sum becomes
multiple times the head)
• r=12%=0.12r = 12\% = 0.12r=12%=0.12
• n=12n = 12n=12 (intensified month to month)
We really want to find ttt.
Substitute the qualities into the recipe:
4P=P(1+0.1212)12t4P = P\left(1 + \frac{0.12}{12}\
right)^{12t}4P=P(1+120.12)12t
Partition the two sides by PPP:
4=(1+0.1212)12t4 = \left(1 + \frac{0.12}{12}\right)^{12t}4=(1+120.12)12t
Compute 1+0.12121 + \frac{0.12}{12}1+120.12:
4=(1+0.01)12t4 = \left(1 + 0.01\right)^{12t}4=(1+0.01)12t
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
Understanding the problem:
Principal amount (P) = R1 500
Interest rate (R) = 6.57% per year
Time (T) = 16 months
Formula for Simple Interest:
Simple Interest (SI) = (P * R * T) / 100
Calculations:
1. Convert months to years: 16 months = 16/12 = 4/3 years
2. Calculate Simple Interest: SI = (1500 * 6.57 * 4/3) / 100 = R131.40
3. Calculate the balance: Balance = Principal + Simple Interest = 1500 + 131.40 = R1631.40
Answer:
The balance in the account 16 months later is R1 631.40.
Therefore, the correct option 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 what amount of time it will require for a speculation to become
multiple times its unique worth with accumulate interest, we utilize the
self multiplying dividends recipe:
A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}A=P(1+nr)nt
Where:
• AAA is the last sum
• PPP is the head (beginning sum)
• rrr is the yearly loan cost (as a decimal)
• nnn is the times the interest is accumulated each year
• ttt is the quantity of years
Given:
• A=4PA = 4PA=4P (in light of the fact that the sum becomes
multiple times the head)
• r=12%=0.12r = 12\% = 0.12r=12%=0.12
• n=12n = 12n=12 (intensified month to month)
We really want to find ttt.
Substitute the qualities into the recipe:
4P=P(1+0.1212)12t4P = P\left(1 + \frac{0.12}{12}\
right)^{12t}4P=P(1+120.12)12t
Partition the two sides by PPP:
4=(1+0.1212)12t4 = \left(1 + \frac{0.12}{12}\right)^{12t}4=(1+120.12)12t
Compute 1+0.12121 + \frac{0.12}{12}1+120.12:
4=(1+0.01)12t4 = \left(1 + 0.01\right)^{12t}4=(1+0.01)12t
