Thread: AQA C2 pg 176. revision exercise last 2 questions

1. AQA C2 pg 176. revision exercise last 2 questions

NOT HOMEWORK!
12. Find the binomial expansion of (1+1/2x)^8 in ascending powers of x up to and including the term x^3. Simplify the coeffiecients as much as possible.

14.The cost of a life insurance policy is £55.89 in the first year. Subsequently the cost in each year is 3% more than the cost in the previous year.

a) Find the cost of the policy in the twentieth year.
b) Find the total of all the payments made by the end of the twentieth year.

2. Originally Posted by ansonbound
NOT HOMEWORK!
12. Find the binomial expansion of (1+1/2x)^8 in ascending powers of x up to and including the term x^3. Simplify the coeffiecients as much as possible.

14.The cost of a life insurance policy is £55.89 in the first year. Subsequently the cost in each year is 3% more than the cost in the previous year.

a) Find the cost of the policy in the twentieth year.
b) Find the total of all the payments made by the end of the twentieth year.
I don't know why this is posted in "Geometry" but ok...

1. $\displaystyle \left(1 + \frac{1}{2x}\right)^8 = \sum_{r = 0}^8{8\choose{r}}(1)^{8 - r}\left(\frac{1}{2x}\right)^r$

$\displaystyle = \sum_{r = 0}^8{8\choose{r}}\left(\frac{1}{2x}\right)^r$.

Now write this out in longhand.

2. Year 0: $\displaystyle C = 55.89$

Year 1: $\displaystyle C = 1.03\cdot 55.89$

Year 2: $\displaystyle C = 1.03 \cdot 1.03 \cdot 55.89$

Year 3: $\displaystyle C = 1.03 \cdot 1.03 \cdot 1.03 \cdot 55.89$.

Can you see that in year $\displaystyle n$ the cost will be:

$\displaystyle C = 55.89 \cdot 1.03^n$.

Now let $\displaystyle n = 20$ and evaluate $\displaystyle C$.