What sum should you deposit into an account to yield 20 year end payments, start

Question

What sum should you deposit into an account to yield 20 year end payments, starting with $10,000 at the end of the first year and increasing by 4% each year at an interest rate of 8% compounded quarterly?

I know you have to calculate the effective interest = [(1 +i)/4]$ = [(1.08)/4]^4 for the compounded quarterly, but this comes out to a negative number. Am I starting this off right? Whatever the interest should come out to I believe you plug it into 1+g'=(1+ieff)/(1+g). Then plug g' into the equation for P should yield the final result asked in the question. Please help and let me know if I am thinking about this properly.

Explanation / Answer

Actually, the formula to calculate effective interest rate is (1+(.08/4))^4-1 =1.02^4-1 = 8.243% Let us call this interest rate, g'. Now, the money you receive at the end if every year using this interest rate is $10,000 Therefore, A*(1+g')=10,000 =>A=10,000/(1+g') =>A= $121,312 Hope this helps

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