Page 113 - Mathematics_Form_3

Sequences and series

Therefore, the amount after 3 years is
A R R
____
1

I = _ = P 1 + ____ R approximately Tshs 252,000.
)
100 ( 100 100
Therefore, Interest I = A − P
3
3
R
____

A = A + P 1 + ____ R = Tshs 252,000 − Tshs 200,000
FOR ONLINE READING ONLY
)
2 1 ( 100 100
= Tshs 52,000 .
R
R
____
= P 1 + ____ + P 1 + ____ R Therefore, the compound interest after

)
(
(
)
100 100
100
three years is Tshs 52,000.
R
R
= P 1 + ____ 1 + ____
)(
)
(
100
100
2
R
= P 1 + ____ Example 4.28
)
(
100
Paula invested a certain amount of
Similarly, the amount of money at the money in a savings account which
end of the third year A is given by
3 provides an interest rate of 10%
3
R
A = P 1 + ____ . compounded annually. After two years,
3 ( 100 ) she had a total of Tshs 50,000.
In general, if n is the number of years, (a) How much did she invest at the
the amount of money at the end of n beginning?
th
year is given by, (b) How much did she receive as
n
R
A = P 1 + ____ and interest interest at the end of the second
n ( 100 ) year?
I = A − P.
n n
Solution
Example 4.27 (a) Given that A = Tshs 50000 ,
2
R = 10, and n = 2 years.
Find the compound interest earned after
Mathematics for Secondary Schools at the interest rate of 8% per annum. Substituting the values into the formula
The formula for computing the
three years on Tshs 200,000 invested
amount is given by,
n
R
____

A = P 1 +

(
)
100
n
Solution
Given P = Tshs 200, 000, R = 8, n = 3.
results into,
n
R
2
____
10
From A = P 1 +
, it implies that
____
(
)
50000 = P 1 +

100
)
(
n
100
3
8
____
(
)
100
3

= 200000 (1 + 0 . 08)
2
3

P (1 . 1) = 50000
A = 200000 1 + Solving for P gives, 50000
______
3
= 200000 (1 . 08)
P =
2
(1 . 1)
= Tshs 251942 . 4
= 41322 . 30
106 Student\s Book Form Three
18/09/2025 09:59:27
MATHEMATIC F3 SB.indd 106 18/09/2025 09:59:27
MATHEMATIC F3 SB.indd 106