Question

A bank pays you 4.5% interest per year. In addition, you receive |100 as bonus at

the end of the year (after the interest is paid). Find a recurrence for the amount of

money after n years if you invest |2000.

Answer 1

The amount of money after 1 year

$$A_1=2000(1+0.045)+100$$

Let $A_{n-1}=$ the amount of money after $n-1$ years, $A_n=$ the amount of money after $n$ years. Then

$$A_n=A_{n-1}(1+0.045)+100, n\geq2$$

A recurrence for the amount of money after n years 

$$A_1=2000(1+0.045)+100=2190$$

$$A_n=A_{n-1}(1+0.045)+100, n\geq2$$