How do I make an explicit formula with below details

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?

 

I don't understand at all.

 

Thank you!

Answer 1

These numbers would make sense if they were related to a bank account that began with one thousand dollar fixed investment, and which grows at 7% compounded annually. But, in reality, the stock market has its ups and downs, which are not a proper mathematical function--there are setbacks of unpredictable nature as well as boons that cannot be foreseen reliably.

 

Taking these numbers at face value, and pretending to believe that the stock market behaves rationally, the compounding formula (annual compounding) is A(t) = 1000(1.07)^t for accumulated amount after t years.  The factor 1.07 consists of 1, which represents retention of the balance, plus 7% growth in one year. This assumes that no 'principal' amount is ever added to the account, only the uniform growth amount.  

Answer 2

You are asking for a geometric series - the sum of a geometric series.

 

S_n = a₁(1 - rⁿ) / (1 - r)

 

For the given data

 

S_n = 1000(1 - 0.07ⁿ) / 0.93

 

To determine each year substitute for n, e.g. for year 5, n = 5.