Question

How much would you need to deposit in an account each month in order to have $50,000 in the account in 5 years? Assume the account earns 5% interest.

Answer 1

Since we are adding a 5% each year, we will proceed as follows, we determine the final percentages and start from "the end to the beginning":

`y_4=50000-50000\cdot0.05\Rightarrow y_4=47500`

Then:

`y_3=47500-47500\cdot0.05\Rightarrow y_3=45125`

And for year two:

`y_2=45125-45125\cdot0.05\Rightarrow y_2=42868.75`

Finally, for the starting year, we will have:

`y_1=42868.75-42868.75\cdot0.05\Rightarrow y_1=40725.3125`

oneedFrom this, we have that the amount of money we need to have in order to get $50 000 in the interest of 5% is approximately $40 725.31.