# Question 1 You are hurt in a car accident and your lawyer wins a R100 000 settlement to be distributed as follows:

R30 000 after ten years

If the lawyer’s fee is R10 000, what is the value of this settlement if the interest rate is 10% per year?

Question 2

You are looking at an investment that has an effective annual rate of 9%. What is the effective?

(a) Semi-annual rate,

(b) Quarterly rate, and

(c) Monthly rate.

Question 3

You have just joined the investment banking firm of Mboweni and Sons. They have offered you two different salary arrangements. You can have R700 000 p.a. for the next two years or R600 000 p.a. for two years along with a R350 000 signing bonus today. The bonus is paid immediately, and the salary is paid in annually in arrears. If the interest rate is 10% p.a. compounded monthly, which salary arrangement do you prefer?

Question 4

Your job pays you only once a year for all the work you did over the previous 12 months. Today, 31 December, you just receive your salary of R50 000 and you plan to spend all of it.  However, you want to start saving for your retirement beginning next year. You have decided that one year from today you will begin by depositing 5% of your annual salary in an account that will earn 11% p.a. Your salary will increase at a rate of 4% p.a. throughout your career. How much money will you have in the date of your retirement 35 years from today?

Question 5

What is the relationship between the value of an annuity and the level of interest rates? Suppose you bought a 10-year annuity of R12 000 p.a. when interest rates are 10% p.a. What happens to the value of your investment if interest rates?

(a) Suddenly drop to 5%, or

(b) Suddenly rise to 15%.

Question 6

You need a 30-year, fixed-rate mortgage of R600 000 to buy your new home. Your bank will lend you the money at 6.8% APR for this 360-month loan. However, you can only afford monthly payments of R3 000 so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at R3 000?

Question 7

You have just purchased a new warehouse. To finance the purchase, you arranged for an 18-year mortgage loan for 80% of the R1.6 million purchase price. The monthly payment on this loan will be R10 000.

(a) What is the APR on this loan?

(b) What is the EAR?

Question 8

You have your choice of two investment accounts. How much money do you need to invest in Investment B today so that it is worth as much as Investment A 15 years from now?

Investment A: 15-year annuity that features end-of-month R2 000 payments and has

an interest rate of 10.5% p.a. compounded monthly.

Investment B: 9% continuously compounded lump-sum investment, also for 15

years.

Question 9

Given an interest rate of 6.5% p.a., what is the value at time period 7 of a perpetual stream of R3 000 payments that will only begin at time period 12?

Question 10

Prepare an amortization schedule for a 5-year loan of R100 000. The interest rate is 20% p.a. and the loan calls for equal annual payments.

(a) How much interest is paid in the third year?

(b) How much interest is paid over the life of the loan?