Question

How much would Babette have accumulated after 15 years?

Babette spends $225 a year on lottery tickets. After 15 years, her total winnings are $1200. Suppose Babette had invested the money she spends on lottery tickets in an account that earns 6% per year compounded annually.

`A={R[(1+i)^n-1]}/i`

Answer 1

I would use the compound interest formula to find the amount of money she earns after 15 years of investing an original amount of $225.

Explanation:

I'm not sure what the variables are for the formula you provided are, so I will go ahead and use a different compound interest formula.

`A=P(1+r/n)^(n*t)` `A=225(1+0.06/1)^(1*15)`
A is the amount earned after investing
P is the principal amount invested
R is the rate of interest
N is the number of times a year the principal is compounded
T is the time in years

Since the original amount (before any interest) is $225, the P would be 225. The rate of interest is 6%, or 0.06. The number of times a year the principal is compounded is 1 because the problem says compounded annually/yearly. The time in years is 15.

Solve by PEMDAS:
`(1+0.06/1)=1.06`

`1.06^(1*15)~~2.397`

`225*2.397=539.325`

The final answer should be around $539.33

Answer 2

After 15 years Babette would have accumulated `$5237.09` from investing her $225 each year into a savings account.

Explanation:

To solve this problem we use the formula which you have given. The purpose of the formula is to find the future value of an annuity (which is a regular payment into an account with compounding interest)

Given your formula;
`A=(R[(1+i)^n-1])/i`
`A` = Future Value of Annuity
`R` = Regular Payment Amount `($225)`
`i` = Interest Rate (as a decimal) `(6%=0.06)`
`n` = Number of Compounding Periods `(n=15)`

Inputing all of this information into the formula yields;
`A=(R[(1+i)^n-1])/i=($225[(1+0.06)^15-1])/0.06`
`A=$5237.09`

I hope this helps :)

Additionally, I have a whole bunch of videos on these exact type of questions on my youtube channel;
https://www.youtube.com/playlist?list=PLSCq2jFAFL0DlI7niQ3cG5CudfeVROhbd
Check it out :)