I am supposed to solve the problem:
A 24-year-old man decides to invest 200,000 euros at a 7% annual interest rate to bring him a regular annual pension from 31 to 50 years inclusive. What will be the pension?
What I did was that I used the formula for the future formula of pension:
$$FV=A\frac{\left ( 1+i \right )^{n}-1}{i}\left ( 1+i \right )=200,000\frac{\left ( 1+0,07 \right )^{7}-1}{0,07}\left ( 1+0,07 \right )=1851960.514$$ and then I divided it for twenty years which is 92598.02
But that is incorrect. The correct solution is 28331.
Can someone tell me, where I made a mistake?
Firstly we need a reference date. I´ve chosen the year when the man is 50 years old. On the LHS the investment is compounded $26$ ($=50-24$) years. On the RHS we use the formula for the geometric series to calculate the future value of $20$ ($=50-31+1$) payments.
$$200,000\cdot 1.07^{26}=x\cdot \frac{1.07^{20}-1}{0.07}$$
$x=...$