QUESTION A

a. The balance on her savings account at the end of year 2 was R72 423.38. At the end of year 5 it was R125 630.41. Determine the balance on her account at the end of year 10. Assume that the interest rate was the same and her savings amount every month was R650.

b. Ivan has one daughter and one son. It is estimated that an average wedding cost R25 000. Assuming 7.5% annual inflation, what would it cost Ivan to pay for his daughters wedding in 16 years?

c. Melvyn has a 30-year policy at Old Mutual. His monthly premium initially was R200 escalating at the start of every year by 10%. Assume that the illustrated growth of the policy was 6% p.a. compounded monthly. His first monthly premium was on January 31, 1999. Determine the maturity value of this policy at the end of the 30 years.

d. Melvyn saved R300 every month since February 1998 at 8% p.a. compounded monthly. At the end of every November he withdraws R3 000 to buy gifts for his wife and children. How much is in that account now, the end of September 2018? Assume that Melvyns 1st withdrawal was in 1999. Assume also that during November, there will only be a withdrawal and no deposit.

e. Dennis won R5 million lottery. The agreement is that the amount will be paid out to him in 5 equal annual payments starting today. Determine the cash value of that winning. Assume that the interest rate will be 9.75% p.a. compounded monthly.

f. Suppose Donovan won R85 million Powerball lottery last night. Assume that Donovan will receive his lottery winnings in 20 equal annual instalments of R4 million each, with the first instalment paid immediately. At the start of the 21st year, the R5 million will be received. If Donavan could invest the funds to yield 9% per year compounded monthly, what is the smallest lump sum that Donavan would be willing to take today in exchange for his 21 instalments?

g. Aunt Georgina retired on her 63rd birthday. Her accumulated pension amount was R2.79 million. Assume that that amount was available to her since her retirement date and that the money was invested with Alexander Forbes. Assume that the account grew at 9.75% p.a. compounded monthly on average. Also assume that she withdrew a maximum regular amount every month from that account as from her 64th birthday with the believe that she will live until the age of 100 years. Aunt Gergina died last week, 2 days after her 91st birthday. Her daughter, Andrea, is the sole beneficiary of the money in that account. How much did Andrea inherit? Assume that there are no other costs.

h. Care facilities are expensive. Lee-Anns mother wants a single room with her own bathroom. The monthly estimated cost is R10 000, but her mother does not anticipate entering the facility for the next four years. Her life expectancy when she enters the facility will be three years. Currently she has R100 000 in assets that are earning 8.75% p.a. compounded monthly. How much must she invest monthly, for the next four years, to meet her anticipated financial needs?

i. Katekani is looking to buy a house and can afford a payment of R14 000.00 a month. If the house costs R1 500 000 and Jane can get a 20 year loan at 10.25% p.a. compounded monthly, how much must Jane give as a deposit to lower her payment to R14 000.00 a month? Give the answer to the nearest next R1000.

j. Fransienas father opened an account, with a once-off amount, in her name some time ago. Fransiena started to deposit R500 into that account on June 25, 1998 and continued to do so every month on the same day of the month until yesterday, September 25, 2018. The account grew at 9.25% p.a. compounded monthly. The account is worth R278 089.23 now. How much was in that account before she deposited that R500 on June 25, 1998?

k. The Parker family, from Banff, Canada, has a 30-year home loan now for exactly 12 years and 5 months. The size of the loan was R3.05 million and the interest rate was 4.5% p.a. for the past 12 years and 5 months. Mr and Mrs Parker accepted a job offer in Kuwait. They plan to sell their house in Canada and relocate. What is the balance on their home loan now? Assume that they paid the minimum required instalment every month. Assume that the Canadian home loan calculation method applies.