A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly.   At the end of 10 years, how much money will he have?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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The man deposit $500. Interrest rate is 5%.

At the end of 1st year he will have 500*(1+5/100)

So at the start of second year he has 500*(1+5/100)

At the end of second year he will have 500*(1+5/100)*(1+5/100) or 500*(1+5/100)^2
So at the end of n years he will have 500*(1+5/100)^(n)
At the end 10 years money in the account = 500*(1+5/100)^10
                                                             = 814.45
At the end of 10 years he will have $814.45 in his account.
This is done in the fundamental way. There are equations to calculate the compount interest directly. It is shown below.
M = P (1+i)^n
M = final amount in the account after n years
P = Initial amount deposited in the account
i = compound interest rate per year
n = Duration in years
For our question;
P= 500
i = 5/100
n = 10
M = 500*(1+5/100)^10 = $814.45