# 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. $A = \frac{R \left[{\left(1 + i\right)}^{n} - 1\right]}{i}$

Jan 8, 2018

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 {\left(1 + \frac{r}{n}\right)}^{n \cdot t}$$A = 225 {\left(1 + \frac{0.06}{1}\right)}^{1 \cdot 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:
$\left(1 + \frac{0.06}{1}\right) = 1.06$

${1.06}^{1 \cdot 15} \approx 2.397$

$225 \cdot 2.397 = 539.325$

The final answer should be around $539.33 Jan 8, 2018 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 = \frac{R \left[{\left(1 + i\right)}^{n} - 1\right]}{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 $\left(n = 15\right)$

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;