## Related questions with answers

Joseph reads a lot about people who are success oriented. He loves to learn about courage, risk taking, and as he describes it, "the road less traveled." His local bookstore has a large business section where he has found biographies of entrepreneurs and maverick corporate leaders. He also finds fascinating some of the books he has seen on financial planning and ways to accumulate wealth. One interesting savings plan he read about challenges the reader to put aside one full paycheck at the end of the year as a "holiday present to yourself." Joseph had never thought about saving in that way, and wondered if it would really accumulate much savings.

Joseph was amazed at how much he could save in this manner and decided to design a detailed savings plan based on projected yearly increases. He realized that he could not start depositing $\$ 1,500$ now, but that he would be able to deposit more than that in the future. If he were able to deposit $\$ 1,000$ at the end of each year for the next 5 years at $8 \%$ compounded annually, $\$ 1,500$ at the end of years $6-10$ at $8 \%$ compounded annually, and $\$ 2,000$ at the end of years $11-35$ at $5 \%$ compounded annually, how much would he accumulate at the end of $35$ years? Assume that any balances from earlier depositing periods would continue to earn the same rate of annual interest. Use the tables for future value of annuities and compound amount.

Solution

VerifiedSince Joseph deposits $\$1,000$ at the end of each year for next $5$ years at $8\%$ annual interest it is an ordinary annuity compounded annually so we need to find the future value of the annuities using given table. To do so, first we need to find the number of interests period and period interest rate as follows:

$\begin{align*} 5\text{ years} \times 1 \text{ period per year}&=5 \text{ periods}\\ \\ \frac{8\% \text{ annual interest rate}}{1 \text{ period per year}}&=8\% \text{ period interest rate} \end{align*}$

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