Mathematics

Question

At the beginning of each year for 14 years, Sherry Kardell invested $400 that earns 10% annually. What is the future value of Sherry's account in 14 years?

2 Answer

  • hmm if I'm not mistaken, is just an "ordinary" annuity, thus 

    [tex]\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\[/tex]

    [tex]\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &400\\ r=rate\to 10\%\to \frac{10}{100}\to &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, so once} \end{array}\to &1\\ t=years\to &14 \end{cases} \\\\\\ A=400\left[ \cfrac{\left( 1+\frac{0.1}{1} \right)^{1\cdot 14}-1}{\frac{0.1}{1}} \right] [/tex]
  • Answer:

    Dependent on which interest plan. On simple interest Sherry Kardell will have a future value of $960 in her account.

    Step-by-step explanation:

    The simple interest is defined as:

    [tex]A=P*(1+r*t)[/tex]

    A is the future amount of money after interest. P is the principal money that is being invested. t is the time that the money is invested and r is that interest rate the money invested to.

    P = $400, r=0.1, t=14 years

    [tex]A=400*(1+0.1*14)=960[/tex]

    Therefore she will have 960-400=$560 more in her account after 14 years.

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