In May 2025
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Thulisile bought a house and managed to secure a home loan for R790 000 with monthly payments of R9 680,70 at a fixed interest rate of 13,75% per year, compounded monthly, over a period of 20 years. If an average yearly inflation rate of 9,2% is expected, then the real cost of the loan (the difference between the total value of the loan and the actual principal borrowed) is
You are saving to pay for your children’s university costs in 20 years’ time. In the first year, your payment is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be
After an accident Nomfundo was awarded an amount from the Road Accident Fund as compensation for her injuries. She chose to receive R18 900 per month indefinitely. If money is worth 9,95% per year, compounded monthly, then the amount awarded is approximately
Moshe will need R145 000 in three years’ time, to open a bakery. He immediately starts to make monthly deposits into an account earning 11,05% interest per year, compounded monthly. Moshe’s monthly deposit is
An amount of R600 is invested every month for eight years. The applicable interest rate is 14,65% per year, compounded quarterly. The accumulated amount of these monthly payments is approximately
Kusho Industries produces and sells computer chips. Its (hourly) production function is 𝒒 = 𝟒𝑲𝟎.𝟒𝑳𝟎.𝟔, while its (hourly) cost function is 𝒄 = 𝟐𝟎𝑳 + 𝟖𝟎𝑲. Furthermore, Kusho must produce 𝒒𝟎 = 𝟒𝟎𝟎 computer chips per hour.
a. Which levels of 𝑳 and 𝑲 satisfy the first-order conditions for the constrained minimisation of Kusho’s
cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrange
multiplier (𝝀). [8]
b. Show that 𝑴𝑹𝑻𝑺 = 𝒘 at the constrained cost minimising levels of 𝑳 and 𝑲 obtained above. [2]
Suppose you are evaluating two mutually exclusive projects, Thing 3 and Thing 4, with the following cash flows:
Thing 3 Thing 4 2000 −$10,000 −$10,000 2001 3,503 0 2002 3,503 0 2003 3,503 0 2004 3,503 19,388 End-of-year cash flows Year
(a)
If the cost of capital on both projects is 5%, which project, ifany, would you choose? Why?
(b)
If the cost of capital on both projects is 10%, which project, ifany, would you choose? Why?
(c)
If the cost of capital on both projects is 15%, which project, ifany, would you choose? Why?
(d)
If the cost of capital on both projects is 20%, which project, ifany, would you choose? Why?
(e)
At what discount rate would you be indifferent between choosing Thing 3 and Thing 4?
(f)
On the same graph, draw the investment profiles of Thing 3 and Thing 4. Indicate the following items:
•
cross-over discount rate
•
NPV of Thing 3 if the cost of capital is 10%
•
NPV of Thing 4 if the cost of capital is 10%
The force of interest is given by: 𝛿(𝑡) = { 0.01 + 0.01𝑡 0 ≤ 𝑡 < 4 0.15 − 0.003𝑡 2 4 ≤ 𝑡 < 6 0.06 𝑡 ≥ 6 (i) Find the expression for the value at time 𝑡 = 0 of a payment of $100 at time 𝑡.
Ajeet Construction Ltd is planning to take a project which initial cash outflow is 100000.The
expected cash inflows from this are tk 40000, tk25,000, tk 20000,tk 35,000, & tk.35000.
Calculate the NPV & IRR of this project, when rate of cost of capital is 15%.
A loan of R125000 is to be amortised by means of 48 equal monthly payments of R2500 starting eighteen months from now. Using Newton's method with the first guess 0.1 the next guess, rounded to four decimal places, is equal to?
