Q3.
[Maximum mark: 61
In this question give all answers correct to two decimal places.
Min deposits 4000 Australian dollar (AUD) into a bank account. The bank pays a nominal
annual interest rate of 6%, compounded semi-annually.
(a) Find the amount of interest that Mia will earn over the next 2.5 years.
Ella also deposits AUD into a bank account. Her bank pays a nominal annual interest rate
of 4%, compounded monthly. In 2.5 years, the total amount in Ella's account will be
4000 AUD.
(b) Find the amount that Ella deposits in the bank account.
13
[31
Answers
Given : Mia deposit 4000 AUD for 2.5 years. at interest rate of 6%, compounded semi-annually.
Ella deposit for 2.5 years. at interest rate of 4%, compounded semi-annually and get 4000.
To Find : the amount of interest that Mia will earn
Ella deposits in the bank account.
Solution:
P = 4000
R = 6% pa = 3 % semi annually
n = 2.5 year = 5 semi Annual years
A = P (1 + R/100)ⁿ
Interest = A - P
A = 4000(1 + 3/100)⁵
=> A = 4,637.1
A - P = 637.1
She will earn $ 637.1
P = P
R = 4% pa = 2 % semi annually
n = 2.5 year = 5 semi Annual years
A = P (1 + R/100)ⁿ
A= 4000
4000= P(1 + 2/100)⁵
=> P = 3,622.92
Ella deposits = 3,622.92 $
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