Annuities & Loan Repayments (Grade 12) — Worksheet & Memo

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Grade 12 · Financial Maths

Annuities & Loan Repayments (Grade 12)

EXAM-STYLE CLASS TEST

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 37

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The FUTURE VALUE annuity formula is …
(1)
A)x[(1 + i)ⁿ − 1]i
B)x[1 − (1 + i)⁻ⁿ]i
C)x(1 + i)ⁿ
D)xi
1.2
The PRESENT VALUE annuity formula is the one to use for …
(1)
A)a loan repaid in equal instalments
B)a savings plan with monthly deposits
C)a single lump-sum investment
D)a simple interest calculation
1.3
A loan is repaid MONTHLY over 20 years at 11% p.a. compounded monthly. Then …
(1)
A)n = 240 and i = 0,11 ÷ 12
B)n = 20 and i = 0,11
C)n = 240 and i = 0,11
D)n = 20 and i = 0,11 ÷ 12
1.4
A tractor bought for R980 000 depreciates at 9,2% p.a. on the REDUCING BALANCE. Its book value after 7 years is …
(1)
A)R498 686
B)R348 880
C)R889 840
D)R666 146
1.5
A fixed amount is deposited at the END of each month for 60 months at 8,35% p.a. compounded monthly, reaching R450 000. The monthly deposit is about …
(1)
A)R6 069
B)R7 500
C)R9 200
D)R76 172
1.6
The OUTSTANDING BALANCE on a loan is found by …
(1)
A)taking the present value of the payments still to be made
B)subtracting the payments already made from the amount borrowed
C)multiplying the instalment by the number of payments left
D)taking the future value of the payments already made
1.7
The total INTEREST paid on a loan equals …
(1)
A)the total of all the instalments minus the amount borrowed
B)the amount borrowed multiplied by the rate
C)the instalment multiplied by the rate
D)the outstanding balance
1.8
A loan of R1 050 000 at 12% p.a. compounded monthly over 25 years has a monthly instalment of about …
(1)
A)R11 059
B)R3 500
C)R11 561
D)R10 500
1.9
If the FIRST repayment is made 6 months after a loan is granted, the loan amount must first be …
(1)
A)grown by compound interest over those deferred months
B)reduced by the deferred months' interest
C)divided by the number of deferred months
D)left exactly as it is
1.10
R12 000 grows to R13 459 in 24 months at m% p.a. compounded QUARTERLY. Then m is about …
(1)
A)5,78%
B)1,44%
C)12,16%
D)5,90%

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[14 MARKS]

Thabo wants to save R450 000 as a deposit for a house. He deposits a fixed amount at the END of every month into an account earning 8,35% p.a., compounded monthly. He makes 60 deposits.

2.1
Write down the values of i and n, and explain why i is not simply 0,0835.
(3)
2.2
Calculate the monthly deposit.
(4)
2.3
Thabo buys a house for R1 500 000 using the R450 000 as a deposit. Write down the value of the loan, and the percentage of the purchase price that he still owes.
(3)
2.4
The loan is taken at 12% p.a. compounded monthly over 25 years, and the monthly instalment is R11 058,85. Calculate the balance outstanding after 21 years.
(4)

Question 3

[13 MARKS]

Thabo plans to buy a car costing R250 000. He pays a deposit of 15% and takes a loan for the balance at 13% p.a., compounded monthly.

3.1
Calculate the deposit Thabo pays, and hence the value of the loan.
(3)
3.2
The FIRST repayment is made 6 months after the loan is granted, and the loan is repaid over 6 years from the date it was granted. Calculate the amount owing when the first repayment is made.
(3)
3.3
Hence calculate the monthly instalment.
(5)
3.4
Explain why deferring the first repayment makes the loan more expensive.
(2)

TOTAL: 37 marks

This question paper consists of 3 questions.