# Rx was invested at 8% per annum compounded half-yearly

Practical

12 – possible answers for

each question is underneath

1. In

January 2009 Klara is a third year student, at the end of the year she will

finish all her courses and receive her degree.

January 2010 she will start working at her dad’s firm. Klara decides that she really needs a car now

and made an arrangement with Toyota to buy a new Toyota for $ 125 000 now and

make the first repayment with her first month’s salary. Toyota offers her an interest rate of 15.5%

per annum compounded monthly. The

repayment period will last for 4 and half years. What will the repayment amount

be?

2. Rx was invested at 8% per annum

compounded half-yearly. After.png”> years one quarter of the total accumulated

amount was withdrawn and the rest reinvested at j % per annum compounded

quarterly. After another .png”> years the new account had increased 1.9 times

and stood at R10141. Find the value of j.

3. How

much must be invested today if you want to receive $15000 at the beginning of

every quarter for the next 11 years from a financial institution that offers

9% effective interest per annum

compounded quarterly.

4. Andrew

wants to buy a second hand car for $60000. He has one of two options: /

Option 1: Borrow $60000 from the bank and pay the

loan back monthly over ‘n period of 4 years.

Option 2: Buy the car for a cash amount of $60000

after first saving an amount monthly for 4 years.

Assume

that the interest is 18% per annum compounded monthly for both options. Which option will be more profitable for Andrew?

5. How

long will it take an amount of $ 5 000 to earn $ 150 interest if a rate of 4 %

per annum simple interest is used?

6. Find

the effective rate of interest per annum equivalent to the nominal interest

rate of 9,8 % per annum compounded quarterly.

7. The

UF estimates that they will need $ 450 000 in one and a half years’ time and

another $ 720 000 in two and a half years’ time to cover the expected cost of

providing each registered student with a dairy.

If interest is calculated at 6,4% p.a., compounded semi-annually, how

much must the UF invest today in order to cover the expected future costs?

8. Mr.

Been invest $ 20 000 at his local bank. It was agreed by the respective parties

that the term of this investment will be 4 years and 7 months and that he will

receive a single payment at the end of this term. Initially interest on this

investment was calculated at an effective rate of 13,5% per annum. After 36

months the bank changed their policy concerning the interest rate so that for

the remainder of the term interest has to be calculated at a rate of 13,5% per

annum compounded monthly. What amount of interest

will Mr. Been receive from his investment?

9. You

decide to save $ 225 at the beginning of each month for the next two and a half

years, which you then plan to use as spending money on a vacation after

completing your studies. The account

into which this money is deposited earns interest at a rate of 9% per annum,

compounded monthly. How much would you have in the bank at the end of the term?

10. Consider a trust

fund of $ 85 000. The conditions of the trust stipulate that 7 years from the

date that the trust fund is set up, one payment should be made per annum over a

period of 10 years to the investor. If this trust earns interest at a rate of

8% p.a. compounded annually, what is the amount of the annual payment that the

investor will receive?

Please

indicate the correct answer:

Question 1

1.

What is the

answer of question 1 in practical 12?

3348.98

3056.56

3032.24

3767.25

Question 2

1.

What is the answer

of question 2 in practical 12?

4%

10%

7%

14%

Question 3

1.

What is the

answer of question 3 in practical 12?

445612.03

468548.27

402584.38

431031.59

Question 4

1.

What is the

answer of question 4 in practical 12?

Option 1

Option 2

Question 5

1.

What is the

answer of question 5 in practical 12?

0.87 years

9 months

8 months

0.82 years

Question 6

1.

What is the

answer of question 6 in practical 12?

8.75%

15.57%

10.17%

13.57%

Question 7

1.

What is the

answer of question 7 in practical 12?

1068003.45

1067002.35

1024507.52

1162035.36

Question 8

1.

What is the

answer of question 8 in practical 12?

16168.44

16180.52

15288.44

167626.44

Question 9

1.

What is the answer

of question 9 in practical 12?

7594.69

8264.69

9028.96

8678.96

Question 10

1.

What is the

answer of question 10 in practical 12?

19089.75

18987.65

21455.75

20101.74

THE NEXT QUESTIONS IS 20

QUESTIONS. KINDLY INDICATE THE CORRECT

ANSWER ONLY:

Question 1

1.

A new

building will need no maintenance for 3years. Thereafter, $ 8 000 will be

needed at the end of each year for the next 30 years for maintenance. Find the

present value of the maintenance of the building, assuming an interest rate of

10% p.a. compounded annually.

$ 69 650.59

$ 82 956.85

$ 1 140.14

$ 56 660.64

None of the above

Question 2

1.

Miss Lucky

won money in the Lotto and she will receive payments of $ 200 000 per year for

20 years at a rate of 10% compounded annually. What is the present value of the

money that she won?

$ 1 062 546.15

$ 1 702 712.74

$ 1 166 557.50

$ 200 109.64

$ 398 172.60

Question 3

1.

Rental on

a DSTV decoder costs $890 per month, payable in advance. What is the cash

equivalent today of 5 years of rental charges, if the interest rate is 11% per

annum compounded monthly?

$ 41 309.03

$ 71 419.83

$ 39 999.30

$ 70 100.00

None of the above

Question 4

1.

A debt

of $8 000 is to be discharged by a series of equal quarterly

payments over 5 years, the first being made immediately. If the

interest rate is 16% p.a. compounded quarterly, find the value of the quarterly

payments.

$ 640.53

$ 705.34

$ 566.00

$ 350.64

Question 5

1.

Mrs.Mandla

pays an insurance premium of R220 in advance every second month (bimonthly) on

an endowment policy with SunLife. The term of the policy is 15 years. Assume

that an interest rate of 14.6% p.a. with 6 compounding periods (bi-monthly) per

annum. How much would she receive on maturity?

R 64 231.53

R 70 568.34

R 71 347.23

R 68 350.64

Question 6

1.

On his 12th birthday Wallace Gromit’s father decides to

give him a lump sum of R 50 000 to invest wherever he wishes. He promises that

on his 16thbirthday he will receive an additional R20000 lump

sum deposited into a standard money market account paying a fixed interest rate

of 15% p.a. compounded annually. Suppose that he knows for a fact that at the

date of his birthday the latest Ford Focus ST (the orange one) will cost R 157

995 (demo model naturally). What nominal annual interest rate will he have to

get on his first investment, if the first investment (only) is compounded

monthly, to be able to afford the car at his 18th

birthday?

17.49%

17.42%

16.23%

None of the above.

Question 7

1.

Mr. Wu, a

first year student at the UFA has won a sum of money from the National Lottery.

He decides to invest some of this money in order to cover his university fees

for his 4th and 5th year respectively. He estimates that he will need $ 30 000

to cover his fees in his 4th year and $ 24 000 to cover his fees in his 5th

year. Suppose he will withdraw the $ 30 000 and $24000 three and four years

respectively from when he opens the

account. How much must he deposit, if the account earns 13% interest per annum,

compounded semi-annually?

$ 35 061.57

$ 14 409.56

$ 23 437.39

None of the above

Question 8

1.

Harry Henn

pays a fixed amount of $R200 at the beginning of each month for a period of

five years towards a savings plan that earns interest at a rate of 15% per

annum compounded monthly. What amount will he receive from this savings plan?

$17 936.34

$1 550.75

$8 512.00

$1 532.98

$17 714.90

$1 348.48

Question 9

1.

Kevin

borrows R 14 400 at an interest rate of 9% p.a. effective for the first 2 years

and then at 11% p.a. compounded annually for the next two years. What will the

amount of the loan be after the four year period?

R 3 328.39

R 37 432.16

R 6 440.98

R 21 079.56

R 9 921.67

Question 10

1.

Suppose

that you invest R 13 000 for 8.25 years into a fund promising the following

returns:

4% p.a. compounded weekly for the first 546 days..gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

12% p.a. compounded quarterly for the next 21 months..gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

9 % p.a. compounded monthly for the next 5 years..gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>.gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>.gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

Assuming 52 weeks in a year, what will the value of the fund be at maturity?

R 25 235.60

R 26 643.81

R 25 805.82

R 17 017.40

Question 11

1.

Ms. Norris

decides to save R850 at the beginning of each month for 4.5 years, which she

plans to use as a deposit on her first car. The account into which this money

is deposited earns interest at a rate of 12% per annum, compounded

monthly. How large a deposit will she have saved in four and a half years?

R 64 785.53

R 70 553.34

R 61 999.,67

R 61 074.59

Question 12

1.

If you

wanted to receive R 10 500 per month for the next 10 and a half years from a

financial institution that offers an interest rate of 8% p.a. compounded

monthly, how much would you have to invest today?

R 106 118.56

R 893 157.86

R 131 241.93

None of the above.

Question 13

1.

Suppose R

8 800 were deposited into an account paying interest of: 16%

p.a. compounded quarterly for the first three years; 14.4% p.a. compounded

monthly for the next three years and 13% p.a. effective thereafter. Find the

balance in the account after 40 months.

R 14 088.80

R 14 777.74

R 21 645.74

None of the above

Question 14

1.

Suppose

that R 12 500 is invested in an account paying the following interest rates:

16% p.a. compounded semi-annually fFor the first 18 months.gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

14.4% p.a. compounded quarterly for the next 27 months..gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

13% p.a. compounded monthly, thereafter….gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>.gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”> .gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>.gif” alt=”https://learn.ufs.ac.za/courses/1/M201602265/ppg/respondus/exam_Tutorial_12_2016/image00257334ab9.gif”>

How long (to the nearest month) in total will it take for the fund to

accumulate to at least a value of R 54 678?

131

130

86

18

Question 15

1.

How much

should be invested at the beginning of each month at a rate of 8.4%

per annum compounded monthly in order to accumulate to R 1650 in 2 years?

R 64.53

R 62.94

R 26.21

R 36.64

Question 16

1.

Lauren is

promised to receive R2 000 in two years time and R3 000 in three years time if

she invests her money with Bank A. If the interest rate is 9% p.a. compounded

monthly, what amount must she invest today?

R 693.33

R 3 964.11

R 5 795.41

R 6 551.72

R 26 083.84

Question 17

1.

A bursary

fund pays R2500 at the beginning of each semester for a period of 4 years to

student D. The account from which these payments are made earns interest at 10%

p.a. compounded semi-annually. What amount was needed in the account at the

beginning of the 4-year period to make these payments possible.

R16 965.93

R15 570.75

R18 512.00

R17 532.98

R19 714.90

R10 348.48

Question 18

1.

Consider a

30 year mortgage where the principle amount is R200 000 and the annual interest

rate is compounded monthly at 6%. What will the monthly payment of this

mortgage be?

R 4 206.10

R 39 253.63

R 202 402.43

R 510 143.46

R 1 199.10

Question 19

1.

Mr. B has

been given an opportunity to receive R 20 000 six years from now and another R

30 000 seven years from now. If he can earn 10% p.a. on this investment, where

interest is compounded quarterly, what amount must he invest today to pay for

this opportunity?

R 693.33

R 3 964.11

R 5 795.41

R 6 551.72

R 26 083.84

Question 20

1.

Suppose

you finance your car with a loan of $ 120 000 at a yearly interest rate of 9%

compounded monthly for four years. How much will your monthly payments on the

loan be?

$ 2 986.21

$ 2 057.23

$ 12 552.66

$ 19 942.76

$ 3 805.44