Question

You have just received an inheritance of $28,000 and would like to invest it into an account. The bank offers two investment plans, one for 4 years at 5.8% compounded annually and another for 3 years at 7.083% compounded annually. You want to make equal annual withdrawals from the account over the life time of the loan. Which investment will yield the highest return over the duration of the loan, given that the account will be zeroed out by the end of that period?

Answer 1

$\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]$

$\bf \qquad \qquad \textit{first investment plan} \\\\\\ \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 28000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5.8\%\to \frac{5.8}{100}\to &0.058\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, meaning} \end{array}\to &1\\ t=years\to &4 \end{cases}$

$\bf -----------------------------\\\\ \left. \qquad \qquad \right. \textit{2nd investment plan} \\\\\\ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 28000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 7.083\%\to \frac{7.083}{100}\to &0.07083\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, meaning again} \end{array}\to &1\\ t=years\to &3 \end{cases}$

see which one yields a bigger "pymt" figure