Question Details

Accumulating Money 
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 book store 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. 
1.	He decided to test the numbers by seeing how much money he would accumulate by a retirement age of 65 if he put one paycheck away at the end of each year. Right now that would mean depositing $1,000 at year-end for the next 35 years. Assuming he makes one yearly deposit of $1,000 at 5% compounded annually, how much interest would he learn?
2.	Joseph was surprised at how large the sum would be and then realized that he would be able to put more money away in the future years because most likely, his salary would go up. He also thought that he could invest the money over the long term at a higher interest rate, so he redid the calculations with a $1,500 annual year-end deposit, at 8% for 35 years. What was his result?
3.	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 in the future. If he were able to deposit $1,000 at the end of the 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. 
4.	By how much does the result differ from the amount calculated above for $1,500 deposited for 35 years ? What accounts for the difference?

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