Question 1 (20 marks) (show all workings)

This question relates to material covered in the Topic 3 on Financial Mathematics. This question addresses the 6^th subject learning outcome.

a. A couple wants to accumulate $10,000 by making payments of $800 at the end of each half year into a savings account that earns interest of 10% per annum. Find the number of full payments required and the size of the concluding payment.

b. A woman wins $200,000 in a lottery. She takes only $20,000 in cash and invests the balance at a rate of interest of 10% with the understanding that she will receive 180 equal monthly payments, with the first one to be made in 4 years. Find the size of the payments.

c. Dr.Ritz has been depositing $4,000 in her savings account every December since 2007. Her account earns 5% compounded annually. How much will she have in December 2017? (Assume a deposit will be made in the year 2017).

d. Mary Tune will receive $20,000 every year for the next 10 years as a payment for a new song she has written. If a 6.0% rate is applicable, should she be willing to sell out her future rights now for $150,000?

e. Mr. Tomas wants to buy an annuity of $1,000 a year for 10 years that is protected against inflation. The ABC Trust Company offers to sell him an annuity where payments increase each year by exactly 10%. Find the cost of this annuity if the rate of interest is 12% per annum.