Question

1) The interest on $120 for 8months is $3.60, find the rate % p.a

2) Pie = 3.14159, e= 2.71828, find pie^2 ÷ e^3 to 3 figures

3) Solve (2x-1)(8x+3)= (4x-1)^2

Answer 1

a)

$$I=P(1+\dfrac{r}{12})^8-P$$

$$3.60=120((1+\dfrac{r}{12})^8-1$$

$$(1+\dfrac{r}{12})^8=1.03$$

$$r=12((1.03)^{1/8}-1)$$

$$r\approx0.04442$$

$4.442\%$

2)

$$\dfrac{\pi e^2}{e^3}=\dfrac{\pi}{e}\approx \dfrac{3.14159}{2.71828}\approx1.16$$

3)

$$(2x-1)(8x+3)=(4x-1)^2$$

$$16x^2+6x-8x-3=16x^2-8x+1$$

$$6x=4$$

$$x=\dfrac{2}{3}$$