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# Discussion problem

If you have \$10 today, you can invest that \$10 and earn interest. If, for example, you earn 5% interest, you will earn \$0.50 interest and have a total of \$10.50 at the end of one year. If you invest the \$10.50 for another year, you will earn \$0.53 interest and have a total of \$11.03 at the end of the second year. In year two, you earned \$0.50 interest on your initial \$10 and \$0.03 interest on the \$0.50 interest earned in year one. Earning interest on interest is called compound interest. The longer you leave your money invested, the greater the compounding effect becomes.

Often times, people project how fast their money will grow and get the idea that they will become so much wealthier sometime in the future. What they often forget is that while their money is growing, the prices of everything they buy are increasing. To really get ahead, your money must grow at a faster pace than the prices of the products you buy.

You can find an additional discussion and time value of money tables in your textbook and/or at, <http://hec.osu.edu/people/shanna/360/timev.htm>. Sherman Hanna of Ohio State University developed these tables.

You would like to take a cruise in six years. The cruise currently costs \$4,250. You expect the price to increase by 4% annually. You can earn 5% on your savings. How much do you need to save at the end of each month so you will be able to afford your cruise in six years?

You invest \$250 in your savings account at the end of each year and earn an average of 6% per year in interest. How much will you have in your savings account at the end of forty years?

You want to have \$40,000 to buy a new boat in six years. How much do you have to save at the end of each year to reach this goal if you earn 5% a year on your savings?

#### Solution Preview

1)You would like to take a cruise in six years. The cruise currently costs \$4,250. You expect the price to increase by 4% annually. You can earn 5% on your savings. How much do you need to save at the end of each month so you will be able to afford your cruise in six years?

Future amount= 4250 x 1.04 ^6= 4250 x 1.27= \$5377.61
Since you can earn 5% on your savings, 5377.61 x ...

\$2.19