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Financial mathematics worksheet

Module by: Pinelands High School. E-mail the author

Financial Mathematics

COMPOUND GROWTH & DECAY – CALCULATING TIME PERIODS (n)

1. After how many years will R1 277 depreciate to R989 if the rate of depreciation is 6% p.a?

2. The price of Gold stocks appreciates 8% annually. Andile currently has gold stock worth R23 712. After how many years will the value of this stock increase to R37 000?

3. After how many years will the accumulated amount be R1350 if R452 is invested at 16% p.a. compounded quarterly?

4. After how many years will an amount of money double if it is invested at 10% p.a., compounded monthly?

5. A company replaces its vehicles when the value has decreased to one quarter of the purchase price. After how long will the replacement take place if annual depreciation of a certain model is estimated to 14,8%?

6. It has been established that the population growth of elephants in a National Park has been increasing at the rate of 6% per year. The park can support a maximum of 500 elephants. Any excess elephants are sold on auction. a) If there are 450 elephants in the park now, after how many years should the owners of the park organise an auction? Round your answer off to the next natural number. b) Using this rounded off number, determine how many elephants will be available for the auction.

1) 4,13 years

2) 5,77 years

3) 7 years

4) 7 years

5) 8,65 years

6) a) 2 years b) 5,62 elephants

FUTURE VALUE OF AN ANNUITY

1. Find the amount of an annuity that consists of 10 annual payments of R6000 each into an account that pays 6% interest per year.

2. Joe, at the age of 32, decided to invest in an annuity. He will put aside R5 000 semi-annually. a) How much will he have at the age of 65 if his rate of return is assumed to be 10% p.a.? b) If Joe had begun his annuity at the age of 22 instead of 32, what would his annuity be worth at the age of 65?

3. How long does it take to save R1 000 000 if you deposit R500 per month in an account paying 7,5% p.a., compounded monthly?

4. The Board of Education takes out a bond of R60 000 000 to build a new school. The Board is required to make payments every 6 months into a sinking fund paying 8% interest per annum compounded semi-annually. At the end of 12 years the Board obligation will be retired. What should the payment at the end of each period be?

5. An Estate Agency purchases a photo-copying machine for R85 000 and realise that they will have to replace it in 4 years time. They predict that the inflation rate will be 8% p.a. and that their machine will depreciate at a rate of 6% p.a. They thus create a sinking fund to take care of the inflation rate. Assuming that they will trade in their present machine, what amount of money must be paid into the fund if the interest rate is 12% p.a. compounded quarterly?

1) R79 084,77

2) a) R2 403 189, 59 b) R6 541 707, 11

3) 418 months OR 35 years

4) R 1 535 209,90

5) R2 444,72

PRESENT VALUE OF AN ANNUITY

1. Bongani buys a car for a down payment of R12 000 and payments of R1 320 per month for 3 years. If the interest rate is 12% p.a., compounded monthly, what is the actual purchase price of the car?

2.Laura wants to invest an amount every two months so that she will have R72 000 in three years’ time to buy a car. The account pays 9% p.a. compounded each second month. How much should she deposit each second month?

3.A couple borrows R500 000 at 9% interest as a mortgage loan on a house. They expect to make monthly payments for 30 years to repay the loan. a) What is the amount of each monthly payment? b) What is the total amount they will pay?

4. Jacob takes a loan of R900 000 from a bank. What will his repayments be if the interest rate is 13% p.a. compounded monthly and he must repay the loan in 10 years?

5.A loan of R50 000 is to be paid off in four equal payments at the end of each quarter in a particular year. Assuming an interest rate of 20%, calculate: a) The amount of each payment. b) The present value of the loan, using the amount from 1. This is to check your calculations. c) The total amount of interest paid

1) R51 741,91

2) R941,02

3) a) R4 023,11 b) R1 448 319,60

4) R13 437,97

5) a) R14 100,59 c) R6 402,36

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