Page 112 - Mathematics_Form_3

Sequences and series

7. Share the pattern you have The amount at the end of the second
determined and the general rule year is:
to other students for further 8000 × 1. 05 + ((8000 × 1. 05 ) × 0. 05 )
discussion.

= (8000 × 1. 05) ( 1 + 0. 05)
FOR ONLINE READING ONLY
The amount of money accumulated
2
= Tshs 8000 × (1.05) .
when invested at a certain interest rate
is a good example of arithmetic and The amount at the end of the third year
geometric progression. Simple interest is:
2
varies directly to time and is given by (8000 × (1.05) (1 + 0 . 05 )
3
the formula: = Tshs 8000 × (1.05) .
I = PRT ,
____
100 Similarly, the amount at the end of the
where P is the principal, R is the interest n year is Tshs 8,000 × (1.05) .
th
n
rate and T is the time. The amounts Tshs 8,000, Tshs

2
For instance, the simple interest payable 8,000 × (1. 05 ), Tshs 8,000 × (1.05)

on Tshs 1,000 at a rate of 15% per annum and so on, are terms of a geometric
will be Tshs 150. The accumulated progression whose first term G equals
1
amount at the beginning of the first year, to Tshs 8,000 and common ratio r equals
second year, third year, fourth year,... will to 1.05.
be Tshs 1,000, Tshs 1,150, Tshs 1,300,
Tshs 1,450, ... These amounts form an Generally, if P is the principal, R is the
AP with common difference of Tshs 150. rate of interest, I is the interest, A is the
Thus, the amount at the beginning of amount after receiving the interest, and
each year is A = 1000 + 150(n − 1). T is the one year period, then
n
For compound interest, after each A = P + I
PRT
interest period, the interest is added to But, I = ____ , where T = 1.
the principal to obtain a new principal Thus, 100
for the next interest year. PR
A = P + ____
Suppose Tshs 8,000 is invested at 5% 100 Mathematics for Secondary Schools
R
interest rate compounded annually. Then, = P 1 + ____ .
(
)
100
the amount at the end of each year is
computed as follows. If time is in years, then the amount at the
If Tshs 8,000 is the principal at the end of the first year is given by
beginning of the first year, then the A = P 1 + R .
____
amount at the end of the first year is: 1 ( 100 )
The amount at the end of the second
8000 + 8000 × 0. 05 = 8000 ( 1 + 0. 05)
year is A + I, where the interest now is
= 8000 × 1. 05 . 1

Student\s Book Form Three 105

18/09/2025 09:59:27
MATHEMATIC F3 SB.indd 105 18/09/2025 09:59:27
MATHEMATIC F3 SB.indd 105