Question

Question 1: [18 marks]
You are considering investing in a scholarship fund for your daughter. The fund operates in the following way:
Starting in one month’s time you would make regular monthly deposits of $50 for a period of eight years into a scholarship fund. Immediately after your final deposit, the fund would pay $10,000 to your daughter to help her with expenses when she commences university study.
a)Illustrate this scenario as a fully labeled timeline diagram. [2 marks]
To be able to compare this fund with other possible investments, you need to know the effective interest rate, j12, that this fund returns.
b)Derive and present the equation of equivalence that is appropriate for this scenario. Do NOT seek to simplify the expression, but rather leave $10,000 as the value of the left-hand side (LHS). [Hint: This is a “Price is Right” problem but with a FV.] [4 marks]
c) Using an estimate of i=1%

Determine the value of the right-hand side (RHS) of the equation of equivalence. Enter this value to 2 decimal places as an answer to “Assignment 1 – Milestones” question 1c.

Answer 1

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Q final return $10,000 months 1 L 3 O qu as 196 1 $50 $50 $50 $50 $50 $50 monthly installment Lei b) i be the monthly interest rate 25 $50 invested få 95 months 5) 50 (1+i) $50 invested for qu months >> 50(1+1) 94 Final $50 invested for months > 50(1+11° 10,000 = s011+ijas 50 (14igay 50 (171) (+i)= K =) 45 Q4. 19000 = 50 K + 50k 10,000 50[14k+t't :-2947 km K95 ]-- 0 By using sum of geometric sequence let Itik + 50 1x11-496) 1+k+k? + kau +k15 1-K 10,000 50(1-K96) Ik so (1-(171)26) sof(143) 96.,). Kalti 10,000 i SOC(+71961) 10,000 the equation required

NC P11. 0.00 . 50 ( (i+0.009-1) 0.01 sy So (1.599273) 00) >> 6 199.30