想問f.3 幾條maths (答到幾多得幾多)

1. if the interest rate is 5% p.a. on simple interest, how long does it take for the amount to be equal to twice the principal?
Let the time required be x years and the principle be P
P(1 + 5x/100) = 2P
1 + 5x/100 = 2
5x/100 = 1
x = 20
It takes 20 years to double
2. Miss Tang deposits some money in a bank at an interest rate of 9% p.a. compounded monthly. After two months, an amount of $73084.05 will be obtained. Find the initial deposit of Miss Tang in the bank.
Let the initial deposit be $x
The monthly interest rate = 9/12 = 0.75%
$x * (1 + 0.0075)^2 = $73084.05
x = 72000
The initial depoit is $72,000
3.A kind of endangered birds decreases by 40% each year. If 1944 endangered birds of that kind are left at present, how many were there 4 years ago?
Let the number of birds 4 years ago be x
x * (1 - 40%)^4 = 1944
x = 1944 / 0.6^4 = 15000
4 years ago, there were 15,000 birds
4. Rate 5% / Property tax 16% / Profits tax - Unlimited companies 16% / limited companies 17.5%

Marco received the notification of demand for rates of his flat for the first quarter of 2004/2005. The quarterly rates payable were $572. Find the rateable value of the flat.
Quarterly rate = $572
Yearly rate = $572 * 4 = $2288
Rateable value - $2288/5% = $45,760

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