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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.

user130306
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  • So after 21 he stops to depositing money? Then you do not need to sum for $F_{65}$. Also, does he get interest from 0 to 21? – garondal Sep 13 '23 at 21:02
  • I was thinking that he does not get the interest from 0 to 21. And my prof asked that I get the value for $F_{65}$ but for my $n$ value I did $65-21=44$ so I don't count the first 21 years. Is that all wrong? – user130306 Sep 13 '23 at 21:07
  • Assume he has $25200$ at the age of 21. The the amout is "just" $25200 \cdot 1.0475^{44}$ after 44 years. – garondal Sep 13 '23 at 21:11
  • hmm so that would be 194168.123. So then the economic growth would be 25200-194168.123=-168968.12 still not understanding how it could be a negative number. – user130306 Sep 13 '23 at 21:15
  • What do you understand under the term "economic growth"? – garondal Sep 13 '23 at 21:21

1 Answers1

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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 $321\,167$.

garondal
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