# Statistics Practical 12: Elementary Interest Calculations Paper

## Statistics Practical 12: Elementary Interest Calculations Paper

Statistics Practical 12: Elementary Interest Calculations Paper

### 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 After years one quarter of the total accumulated amount was withdrawn and the rest reinvested at j % per annum compounded quarterly. After another 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?

# 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?

Question 3

1. What is the answer of question 3 in practical 12?

 445612 468548 402584 431032

Question 4

1. What is the answer of question 4 in practical 12?

### Statistics Practical 12: Elementary Interest Calculations Paper 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?

 1.068e+06 1.067e+06 1.02451e+06 1.16204e+06

Question 8

1. What is the answer of question 8 in practical 12?

 16168.4 16180.5 15288.4 167626

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?

 19089.8 18987.7 21455.8 20101.7

### THE NEXT QUESTIONS IS 20 QUESTIONS. KINDLY INDICATE THE CORRECT ANSWER ONLY:

#### Statistics Practical 12: Elementary Interest Calculations Paper Question 1

1. A new building will need no maintenance for 3 years. 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

## ORDER Statistics Practical 12: Elementary Interest Calculations Paper

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.

### Statistics Practical 12: Elementary Interest Calculations Paper 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.   12% p.a. compounded quarterly for the next 21 months.   9 % p.a. compounded monthly for the next 5 years.        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   14.4% p.a. compounded quarterly for the next 27 months.   13% p.a. compounded monthly, thereafter…        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?

## ORDER Statistics Practical 12: Elementary Interest Calculations Paper

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

## Statistics Practical 12: Elementary Interest Calculations Paper 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

Statistics Practical 12: Elementary interest calculations