Page 114 - Mathematics_Form_3

Sequences and series

Therefore, Paula invested where A denotes total amount
n
Tshs 41322 . 30 . accumulated
Since the amount after two years was P denotes Principal
Tshs 50,000, R denotes interest rate
n denotes number of years of
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Interest, I = A − P
n compounding the interest
= Tshs 50000 − Tshs 41322 . 30 t denotes number of times the
= Tshs 8677 . 70 interest is compounded per year
Therefore, the compound interest was Example 4.30
Tshs 8677.70.
A business person deposited 800,000
Tanzanian shillings in a bank account
Example 4.29 paying 6% interest compounded semi-
annually. What will be the total amount
Find the amount of money at the end of after 5 years?
5 years after investing 50,000 Tanzanian
shillings at a compound interest rate of Solution
5% annually. Given P = Tshs 800,000, n = 5 years,
R = 6%, t = 2.
Solution nt
Given that P = Tshs 50,000, R = 5%, From A = P   1+ R   , it implies that:
n
and n = 5 years , then amount A at a  100t  25×
n

given period of time is given by, A = 800000 1+ 6  

5
n  100 2  ×
R
A = P 1 + ____
10
n ( 100 ) = 800000 (1 . 03)
5
5
____
= 50000 1 + = 1,075,133 .10
)
(
100
Therefore, the amount after 5 years is
= 50000 (1 + 0 . 05) 1,075,133.10 Tanzanian shillings.
5
= 63814.08
Hence, the amount at the end of 5 years
will be 63,814.08 Tanzanian shillings. Exercise 4.9 Mathematics for Secondary Schools
1. Find the amount of money at the
Note that, compound interest can be end of two years and three years if
compounded semi-annually, quarterly, 1,200,000 Tanzanian shillings is
monthly and so on. In this case, the invested at 6% compounded annually.
following formula is used: 2. Find the interest for a principal of

A = P   1+ R   nt 1,000,000 Tanzanian shillings at
4% interest compounded annually
n
 100t  after 10 years.

Student\s Book Form Three 107

18/09/2025 09:59:28
MATHEMATIC F3 SB.indd 107 18/09/2025 09:59:28
MATHEMATIC F3 SB.indd 107