Chapter 1.4, Problem 9G

Account 1: You deposit $1,000 into an account that pays 5% simple interest on that $1,000 each year.

Account 2: You deposit $1,000 into an account that pays 5% of the account balance at the beginning of the current year in interest each year.

Here’s a way to describe the difference in growth of the two accounts: Account 1 increases in value by every year, while Account 2 has its value multiplied by every year. So the value of Account 1 at any time looks like $\mathrm{\$\; <mn>\; 1\; <mo>\; ,\; <mn>\; 000\; <mtext>\; \; <mo>\; +\; <mtext>\; \; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mtext>\; \; <mo>\; \times \; <mtext>\; \; <mrow>\; <mo>\; (\; <mrow>\; <mtext>\; the number of years passed\; <mo>\; )\; <mo>\; ,\; </mo>\; </mo>\; </mtext>\; </mrow>\; </mo>\; </mrow>\; </mtext>\; </mo>\; </mtext>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mtext>\; </mo>\; </mtext>\; </mn>\; </mo>\; </mn>}$ and the value of Account 2 at any time looks like $\mathrm{\$\; <mn>\; 1\; <mo>\; ,\; <mn>\; 000\; <mrow>\; <mo>\; (\; <mrow>\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; )\; <mrow>\; <mo>\; (\; <mrow>\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; \_\; <mo>\; )\; <mtext>\; \; <mo>\; .\; <mtext>\; \; <mo>\; .\; <mtext>\; \; <mo>\; .\; <mo>\; ,\; </mo>\; </mo>\; </mtext>\; </mo>\; </mtext>\; </mo>\; </mtext>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mrow>\; </mo>\; </mrow>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mo>\; </mrow>\; </mo>\; </mrow>\; </mn>\; </mo>\; </mn>}$ where the multiplication occurs the same number of times as the number of years that have passed.