Financial Maths

Mathematics

Financial Maths

Grade 10

Question 1: A student buys a TV set of R11 000 on a hire purchase agreement. He agrees to pay a deposit of 20% and the balance over a period of two years in monthly instalments at 14% simple interest p.a. He also takes out an insurance premium of R18,50 per month. Determine the amount of each instalment. Question 2: Mikayla wants a new Polaroid camera. It costs R1 750, but her parents said she must buy it herself. She finds out that Hot Gadgets has a hire purchase contract at 11.5% interest for 3 years. She will need to pay a 15% deposit.

2.1 What will she have paid at the end of 2 years in total? 2.2 Calculate the monthly instalments. 2.3 After some more research on the internet, she saw

that Amazon sells one at $95. But she needs to pay the shipping fees of $15 as well. What will the camera cost if the Rand/Dollar exchange rate is R13,99 per dollar? Take the shipping cost into consideration when calculating your answer. 2.4 Which option would be the best financially for Mikayla? Amazon or Hot Gadgets? Give a reason for your answer. 2.5 What will the cost of the camera be in 5 years if the inflation rate is 7,2 % per year? (use the Hot Gadgets amount) Question 3: A savings account is opened with an amount of R45 000 and three years later R23 000 is withdrawn. Six years after the account is opened, R11 000 was deposited. The interest rate was as follows: 6,5% per annum compounded yearly for the first five years and 4,2% per annum compounded yearly for the remainder of the period. Calculate the balance at the end of 10 years.

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Mathematics

Grade 10

Question 4: 4.1 Alex deposited R120 000 into a savings account. Four years later he added R6 000. The

interest is 9%, compounded annually for the first 3 years and then 7% compounded annually for the rest of the time. What total amount will he have at the end of 8 years? 4.2 If Alex wants 200 000 in his savings account at the end of 8 years, what should the compounded interest rate be if he invests 120 000 (rounded to two decimal places)? Question 5: 5.1 If the exchange rate between Rand and American Dollar is 11,83: $1, and the exchange rate between Rand and British pound is 14,95: ?1, find the exchange rate between $ and ?. 5.2 Thabo buys a car radio costing 1 750 on hire purchase and pays a deposit of 170. He then pays 24 monthly payments of 75. Calculate: 5.2.1 The total simple interest paid (the amount). 5.2.2 The rate of simple interest. Question 6: Read the advertisement carefully and use the information in it to calculate the following question:

CHEETAH'S SHARE BANK

JOIN THE BAND OF HAPPY SAVERS. BEST RATES IN THE LAND: 10,05% p.a. simple interest. 6.1 Ryan invested 20 000 in the Cheetah's Share Bank for 3 years. How much money did he receive at the end of the investment period?

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Mathematics

Grade 10

6.2 Bernie wants to travel overseas when she finishes her studies in 4 years' time. She needs 38 500 to do so. She has already saved 11 210. What rate of compound interest per year must she get to achieve her aim? (Correct to one decimal place.)

6.3 On a trip to New York, Taylor booked into a hotel for three nights. The exchange rate at that time was $1 = 9,10. The cost per night was $450. How much did she spend in Rands for the three nights?

Question 7: Dylan is furnishing his townhouse and has chosen the sofa he wants. It costs 7 999 if he pays cash for it. He has chosen to buy it on hire purchase on the following terms:

? Deposit of 900. ? 24 months to pay it off. ? At a rate of 25% per annum. Calculate his monthly instalments. Question 8: Zukiswa wants to triple her money in 4 years. At what interest rate, compounded monthly, does she need to invest the money (as a percentage to two decimal places)? Question 9: Karabo inherits some money from a relative and he decides that he would like to invest his money. He looks at the interest rates of the following accounts at FNB and Standard Bank:

9.1 If Karabo decides to invest 200 000, which account will earn him the most interest? 3

Mathematics

Grade 10

9.2 Karabo eventually decides to invest the money in the FNB Money on Call account. Calculate how much money Karabo will have in his account after 2 years.

9.3 If Karabo wants to buy a car that sells for 210 500 and the rate of depreciation is 17% per annum, then calculate how much the car will be worth in 2 years' time.

9.4 If the current average rate of inflation is 9,2% per annum, calculate the cost of the same car in 2 years' time.

Question 10: Fill in the missing values in the following table.

Compounding Period

Principal

Annually Semi-

annually Quarterly Monthly Quarterly Quarterly

R1 000 R1 000

R500 R350 R800 R 1 250

Yearly rate

9% 9%

Time

5 years 5 years

Period rate (the interest

paid per compounding

period)

Number of periods

8%

3 years

12%

5 years

12%

90 days

16% 450 days

Total Interest

Total Amount

* Question 11: Imagine that you save 1 370,50 per month at an interest rate of 5% per annum compounded monthly for 2 years in a savings account. Use the formula below to calculate how much you would save in total.

=

[(+)-]

,

where

F

is

the

total,

is

the

monthly

interest

as

a

decimal,

is

the

Monthly savings amount and is the number of months.

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Mathematics

Grade 10

MEMORANDUM Question 1: A student buys a TV set of R11 000 on a hire purchase agreement. He agrees to pay a deposit of 20% and the balance over a period of two years in monthly instalments at 14% simple interest p.a. He also takes out an insurance premium of R18,50 per month. Determine the amount of each instalment. Deposit: 20% ? 11 000 = 2 200 Balance: 11 000 - 2 200 = 8 800 = (1 + ? ) = 8 800(1 + 0.14 ? 2) = 11 264 ? 24 = 469,33 469,33 + 18.50 = 487,83 Question 2: Mikayla wants a new Polaroid camera. It costs R1 750, but her parents said she must buy it herself. She finds out that Hot Gadgets has a hire purchase contract at 11.5% interest for 3 years. She will need to pay a 15% deposit. 2.1 What will she have paid at the end of 2 years in total?

Deposit: 15% ? 1 750 = 262,50 Balance: 1 750 - 262,50 = 1 487,50 = (1 + ? ) = 1 487,50(1 + 0,115 ? 3) = 2 000,69 + 262,50 = 2 263,19 2.2 Calculate the monthly instalments. 2 000,69 ? 36 = 55,57 2.3 After some more research on the internet, she saw that Amazon sells one at $95. But she needs to pay the shipping fees of $15 as well. What will the camera cost if the Rand/Dollar exchange rate is R13,99 per dollar? Take the shipping cost into consideration when calculating your answer. Amazon: $95 + $15 = $110 Rand : Dollar 13,99 1

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