Need an formula/equation for this scenario

[gwanun]

Homework Statement

I invest 600 every year for 8% compound interest
for etc. first yr 600* 1.08= 648

2nd yr
600+648= 1248
1248*1.08= 1347.84

3rd yr
1347.84+600=1947.84
1947*1.08=2102.74

and so on

Homework Equations

compounded interest formula is

P is the principal (the money you start with, your first deposit)

r is the annual rate of interest as a decimal (5% means r = 0.05)

n is the number of years you leave it on deposit

A is how much money you've accumulated after n years, including interest.

If the interest is compounded once a year:

A = P(1 + r)power of n

The Attempt at a Solution

i attempted A= nP(1+r)power of n

but there's some difference in the answers I am getting

please help correct my formula

 

[gwanun]

nvm i got it

P = sum deposited at the end of each year (beginning one year from when the annuity "starts")

r = the interest rate, as a decimal (5%, for example, is r = 0.05)

n = number of years the annuity has run

N = total amount accumulated at the end of n years.

N = (P/r)( (1 + r)n - 1)

 

[Architeuthis Dux]

Your formula is close, but there are a few errors. The correct formula for compound interest is:

A = P(1 + r)^n

Where:

A = amount accumulated after n years
P = principal (initial investment)
r = annual interest rate (as a decimal)
n = number of years

In your attempt, you are using n as the principal and adding the principal to the accumulated amount each year, which is incorrect. Also, remember to use the same units for the interest rate and time (e.g. if the interest rate is given as 8% per year, n should be in years as well). So for this scenario, the correct formula would be:

A = 600(1 + 0.08)^n

Where n is the number of years (starting with n=1 for the first year).

Using this formula, the answers should match with the ones you provided in the homework statement.