How do I make an explicit formula

Question

How do I make an explicit formula based on 7% annual return. It says to convert 7% to decimal and add 1. The starting amount of the account is $1,000.

I need to figure out how much money I would have every year for 10 years.

Can you please show me exactly how the formula should look and how much money would I have in year 1 and year 2?  Hopefully I can figure out the rest of the years from there.

I don't understand at all, so I need it written exactly how it should look.

Answer 1

If it increases at an annual rate of 7%, then at the end of each year, it is 7% higher than the amount at the start of the year.  That means you end the year with an extra 7%, which, i.e. 107% of the starting amount, or 1.07 times the starting amount.

 

After 1 year:  $1000 (1.07) = $1000 (1.07)¹

 

After 2 years:  [$1000 (1.07)] (1.07) = $1000 (1.07)²

 

After 3 years:  [$1000 (1.07)²] (1.07) = $1000 (1.07)³

 

Do you see the pattern?  After n years, the amount is $1000 (1.07)ⁿ.