When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $1000 at the end of the first year and increase by $10 each subsequent year?

$1,109.62

Step-by-step explanation:

Let's first compute the future value FV.  

In order to see the rule of formation, let's see the value (in $) for the first few years

End of year 0

1,000

End of year 1(capital + interest + new deposit)

1,000*(1.09)+10  

End of year 2 (capital + interest + new deposit)

(1,000*(1.09)+10)*1.09 +10 =

End of year 3 (capital + interest + new deposit)

and we can see that at the end of year 50, the future value is

The sum  

is the sum of a geometric sequence with common ratio 1.09 and is equal to

and the future value is then

The present value PV is

rounded to the nearest hundredth.