Someone deposits 100 a month into an account from year 0 to 21, then he stops depositing after year 21 and allows it to grow to age 65 at an interest rate of 4.75% per year.
I need to calculate $F_{65}$. Then I need to identify how much money was deposited in total and then calculate the economic growth.
My work:
$F=A*\frac{(1+r)^{n}-1}{r}=100*\frac{(1+0.0475)^{44}-1}{0.0475}\approx 14115.96685$
Then the total deposit is $100*12*21=25200$
The economic growth is the final amount - the total deposit
So the growth is $14115.96685-25200=-11084.03315$
Is this right? I don't understand how you can't have a positive amount of growth if all you did was deposit money and then let it sit there.
From 0 to 21 the person deposits 1200 per year:
$$1200 \cdot \frac{1.0475^{21}-1}{0.0475}\approx 41682.5$$
This amoout is for 44 years on the bank
$\approx 41682.5 \cdot 1.0475^{44} \approx 321\,167$
If there would be no interst, the person would have only $25\,200$ instead of $321\,167$.