Cambridge International Mathematics

Topics in arithmetic (Chapter 10) 223

Example 20 Self Tutor

How much do I have to invest now at 9%p.a. compound

interest, if I want it to amount toE10 000in 8 years’ time?

Suppose the amount to be invested now isEx.

) x£(1:09)^8 = 10 000

) x=

10 000

(1:09)^8

¼ 5018 : 6628

So, I need to invest aboutE 5020 now.

Example 21 Self Tutor

An investment of$ 5500 amounted to$ 8000 after 4 years of

compound growth. What was the annual rate of growth?

If the annual multiplier wasx, then 5500 £x^4 = 8000

) x^4 =

8000

5500

) x=

4

r

8000

5500

¼ 1 :098 201

) x¼ 109 :82%

So, the annual growth rate was 9 :82%.

EXERCISE 10F

1 Find the final value of a compound interest investment of:

a $2500after 3 years at6%p.a. with interest calculated annually

b $ 4000 after 4 years at7%p.a. with interest calculated annually

c E 8250 after 4 years at 8 :5%p.a. with interest calculated annually.

2 Find the total interest earned for the following compound interest investments:

a E 750 after 2 years at 6 :8%p.a. with interest calculated annually

b $3350after 3 years at 7 :25%p.a. with interest calculated annually

c $12 500after 4 years at 8 :1%p.a. with interest calculated annually.

3 Xiao Ming invests12 000Yuan into an account which pays7%p.a. compounded annually. Find:

a the value of her account after 2 years b the total interest earned after 2 years.

4 Kiri places$5000in a fixed term investment account which pays 5 :6%p.a. compounded annually.

a How much will she have in her account after 3 years?

b What interest has she earned over this period?

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Y:\HAESE\IGCSE01\IG01_10\223IGCSE01_10.CDR Tuesday, 28 October 2008 1:36:39 PM PETER