Daisy invested 37 000 Australian dollars (AUD) in a fixed deposit account with an annualinterest rate of 6.4 % compounded quarterly.(a) Calculate the value of Daisy’s investment after 2 years. [3]After m months, the amount of money in the fixed deposit account has appreciated to morethan 50 000 AUD.(b) Find the minimum value of m , where mℕ
Question
Daisy invested 37 000 Australian dollars (AUD) in a fixed deposit account with an annualinterest rate of 6.4 % compounded quarterly.(a) Calculate the value of Daisy’s investment after 2 years. [3]After m months, the amount of money in the fixed deposit account has appreciated to morethan 50 000 AUD.(b) Find the minimum value of m , where mℕ
Solution
(a) The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, P = 37,000 AUD, r = 6.4/100 = 0.064 (converted from percentage to decimal), n = 4 (since interest is compounded quarterly), and t = 2 years.
Substituting these values into the formula, we get:
A = 37,000(1 + 0.064/4)^(4*2) A = 37,000(1 + 0.016)^
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