PDF Worksheet 15 - Financial Math .za

[Pages:2]Worksheet 15 - Financial Math

What you have to know

? The compound interest formula S = A(1+i)n. This is future value of a single investment.

? So A = S(1 + i)-n. This is the present value, i.e. how much in bank now to get S after n periods (for a single investment)

?

sni

=

(1

+

i)n i

-

1

.

It

means

the

amount

that

will

be

in

the

bank

if

you

invest

R1 for each of n periods at rate i.

So if you invest R each time you have

S = Rsni.

Called the amount. It's just the future value.

?

ani

=

1

-

(1

+ i

i)-n

.

This is the present value of the annuity It means how much

must you have now to make payments of R1 at end of each period.

? So, if you want to make payments of R it is just

Called the value.

A = Rani

Exercises

1. If R500 is invested at 7% compounded annually what will the investment be worth after 5 years?

2. If R800 is invested at 8% compounded quarterly what will the investment be worth after 6 years? What is the effective rate of interest?

3. If R10 000 is invested for 6 years compounded monthly, the investment will be worth R15 661.17.

(a) What is the nominal interest rate? (b) What is the effective rate of interest?

4. I invested R400 at an annual rate of interest of 6%. The investment is now worth R535.29. For how long was the money invested?

5. I invested R1 000 000 four years ago. The investment is now worth R1 200 000. Interest was calculated quarterly.

(a) How many periods are there? (b) What was the nominal rate of interest?

6. R1234 is invested now for n years at rate i. The investment is then worth R5678.

(a) What is the future value of the investment of R1234 after n years? (b) What is the present value of the R5678 now?

7. (a) How much should be invested now if the amount is to be worth R500 in one year's time, where the nominal rate is 8% compounded annually?

1

(b) What is the present value of R500 due in 1 year's time where interest rate is 8% compounded annually?

8. (a) I invest R100 on Jan 1 2009 at a rate of 8% compounded monthly. How much will it be worth on Dec 31 2010?

(b) I invest another R100 on Jan 1 2010 at the same rate of 8% interest. How much will it be worth on Dec 31 2010?

(c) How much do I have altogether on Dec 31 2010?

(In case you have not understood, this is an annuity with only 2 payments. It's easier to work them out separately. But if there are lots of payments ...)

9. (a) I invest R250 at the end of each month for 2 years at a nominal interest rate of 9% compounded monthly. How much is the investment worth at the end?

(b) How much money did I invest altogether?

(c) How much have I gained from interest?

So if (a) above had multiple choice answers of

(i) R5472.29 (ii) R8514.61 (iii) R6547.12 (iv) R6831.61

then (i) is absurd (it's what you get from wrong formula), since interest would be negative; (ii) is miles too high.

10. I want to make monthly payments to my ex-wife of R5000 per month over the next 10 years (after which I hope she has found another man). The interest rate is 10% compounded monthly. How much must I have in the bank now?

11. I borrow R850 000 to be paid off over 5 years in monthly installments. The interest rate is 12% compounded monthly. How much are the repayments?

12. I wish to buy a house for R1 000 000. I make a deposit of R200 000 and then monthly payments of R7500. The interest rate is 9% compounded monthly. How long will it take before I have paid off the debt?

13. A student needs fees of R30 000 per year, to be paid at the start of each year for 3 years. She will also need R5 000 per month living expenses, starting now. Interest is calculated at 8% compounded monthly.

(a) What is the effective interest rate? (b) How much capital must parents have to pay the fees? (c) How much capital must parents have to pay the living expenses? How much capital

do the parents need altogether?

14. I wish to buy a house for R1 500 000. I make a deposit of R400 000. Monthly repayments are R20 000, starting in 1 year's time, and interest is compounded monthly at 9%. For how long will the repayments continue?

Answers

1. R701.28

2. R1286.75, 8.24%

3. (a) 7.5% (b) 7.76%

4. 5 years

5. (a) 16 (b) 4.58%

6. (a) R5678 (b) R1234

7. (a) R462.96 (b) R462.96

8. (a) R117.29 (b) R108.30 (c) R225.59

9. (a) R6547.12 (b) R6000 (c) R547.12

10. R378 355.82

11. R18 907.78

12. About 18 years

13. (a) 8.3% (b) R53 278.70 (c) R160 622.80 (d) R243 901.50

13. About 80 months (6 year and 8 months).

2

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download