 # Essays on MAF101 - Fundamentals Of Finance Math Problem

Qs1 (a). (Option 1) effective rate (ie) = [(in + 1)1/n ]- 1 (Grinols, 2001). ie = [(0.105+1)1/365]-1ie = (1.105)0.00274-1ie = 0.027%(Option 2) effective rate = [(0.1055+1)1/4] – 1 Effective rate = (1.1055)0.25 – 1Effective rate = 0.0254 or 2.5%(Option 3) effective rate = [(0.095+1)1/2] – 1Effective rate = (1.095)0.5 – 1Effective rate = 4.64%The best source of finance from the effective rates calculated is ABC Friendly Finance Company. (b) Total payment at the end of fifth year will be; Interest payment = (1000000*0.0475*10)Interest payment = 475000Total payment =1000000+475000+1000Total payment = 1476000Nominal rate = [476000/ (1000000*5)]*100Nominal rate = 9.52%Effective rate = [(0.0952+1)1/2)]-1Effective rate = (1.09520.5) - 1Effective rate = 4.65%(c) Nominal rate = real rate + rate of inflationReal rate = nominal rate - rate of inflation (Grinols, 2001). Real rate = 10.5% – 3%Real rate = 7.5%Next year nominal rate of return = 7.5% + 3%+ 3.5%Nominal rate will be = 14%Qs 2.

(a) Principal = \$10 millions, rate = 0.12, t = 10 years and n = 12A = p (1 + r/n)t*nA = 10000000(1 + 0.12/12)10*12A = 10000000(1.01)120A = \$33003868.945Monthly payments = 33003868.945/ (12*10)Monthly payments = \$275032.241(b) At the 40th payment, the balance will be; 33003868.945 – (275032.241* 40) = 33003868.945 – 11001289.64Balance payment = \$22002579.305(c) Total payment periods are 120.

Thus, 40th payment represents (40/120 * 100) = 33.33% of the principal and interest payment. Remaining principal amount not yet covered amounts to; (10000000* 0.6667) = 6667000Remaining payment periods = 120- 40 = 80A = 6667000(1 + 0.15/12)80A = 6667000(1.0125)80A = 48066188.63Monthly payments = 48066188.63/ 80Monthly installment payment = \$48066188.63 Qs 3. (a) Future value = \$600,000 and real rate of interest is = 5% At 19 years old; t = 60 – 19 = 41600000 = p. v (1 + 0.05/1)1*41600000 = p. v (1.05)41600000 = p. v*7.391p. v = 600000/ 7.391p. v = \$81179.8133 (ii) At 23 years old; t = 60 – 23 = 37600000 = p. v (1 + 0.05/1)1*37600000 = p. v (1.05)37600000 = p. v* 6.0814p. v = 600000/ 6.0814p. v = \$98661.4924(b) Annuity payment; w = [p. r (1+ r)n-1]/ (1+r)n-1(i) At 19 years; w = [600000* 0.05(1+ 0.05)41-1]/ (1+0.05)41 -1W = [30000* (1.05)40 ]/ (1.05)41 – 1W = (30000* 7.039988)/ (7.3919881 – 1)W = 211199.64/ 6.3919881W = \$33041.31At 23 years; W = [(600000* 0.05(1+ 0.05)37-1]/ (1+0.05)37 -1W = [30000 (1.05)36]/ (1.05)37 – 1W = [30000* 5.791816]/ (6.081406943 – 1W = 173754.48/5.081406943W = \$34194.167(c) (i) At 19 years; w = [600000* 0.045(1+ 0.045)41-1]/ (1+0.045)41 -1W = [27000* (1.045)40]/ (1.045)41 – 1W = (27000* 5.8163645)/ (6.0781 – 1)W = 157041.842 / 5.0781W = \$30925.315c.

(ii) At 23 years; W = [(600000* 0.045(1+ 0.045)37-1]/ (1+0.045)37 -1w = [27000* (1.045)36]/ (1.045)37 – 1w = (27000* 4.877)/ (5.09686 – 1)w = 131679/ 4.09686w = \$32141.445(d) At 19 years; w = \$33041.31;10% of 33041.31 = 3304.131Total annuity = 33041.31 + 3304.131 = 36345.231At 60 years old = 36345.231* 41 = \$1490154.471At 23 years W = \$34194.167; 10% of 34194.167 = 3419.4167Total annuity = 34194.167+ 3419.4167 = 37613.5837At 60 years saving will be = 37613.5837* 37 = \$1391702.60Qs 4.DUP FUND MANAGEMENT MEMORANDUM To: Dup#2 fund clients. From: Nigel Tan, Manager. Date: 28 April 2012Subject: Australia ordinary stock return in the year 2008 in relation to foreign investment. IntroductionAt the end of annual meeting on 28 December 2011, members requested to be informed the reasons why the fund investment firm trades in the international stock market.

This was as a result of the some of the members opinion that the returns in Australian stock market is highly correlated to stock market of other developed market. BackgroundIn 2008, fund investment across international stock market generated a loss of 25% in return. The firm has not recovered the loss since then and this has prompted members to be dissatisfied as to why they should continue having their funds diversified across the international stock market. The stock market investment average return at the Australia stock market from our finding showed that the market also registered a loss of 4.46% in the year 2008.

Average stock return in Australia stock marketThe average returns findings for the year 2008 on monthly basis is as shown below (Yahoo! Finance: more on ^AORD. Historical cost 2008). DateOpenCloseReturn12/1/20083669.83659.3-0.0028611/3/200840033672.7-0.0825110/1/20084662.43982.7-0.145789/1/20085209.24631.3-0.110948/1/20085047.45215.50.0333047/1/20085345.85052.6-0.054856/2/200857745332.9-0.076395/1/20085654.25773.90.021174/1/20085416.156570.0444783/3/20085639.35409.7-0.040712/1/20085717.25674.7-0.007431/2/20086418.65697-0.11242Average -0.04458The average returns for the year 2008 shows that, if the fund investors had invested only in the Australia stock exchange, they would as well have incurred a loss. The loss nevertheless, would not have being as high as the one the fund investors incurred that same year.