At the beginning of the year 2000, Bob put $100 in a savings account. The bank pays Bob 5% interest on his total savings at the end of each year, including all interest added to the account. Assume the interest rate continues and Bob does not deposit any additional money in the account. How much will he have in his savings account, to the nearest cent, after 5 interest payments?

To find out how much Bob will have in his savings account after 5 interest payments, we can use the formula for compound interest, because the interest the bank pays is added to the balance, which then earns more interest.

The compound interest formula is:

A = P(1 + r/n)^(nt)

Where: - A is the amount of money accumulated after n years, including interest. - P is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal). - n is the number of times that interest is compounded per year. - t is the time the money is invested or borrowed for, in years.

For Bob's case: - P = $100 (initial deposit) - r = 5% or 0.05 as a decimal - n = 1 (interest is compounded once per year) - t = 5 years

Let's calculate it:

A = 100(1 + 0.05/1)^(1*5) A = 100(1 + 0.05)^5 A = 100(1.05)^5 A = 100 * 1.2762815625 (Using a calculator for 1.05^5) A = $127.63 (after rounding to the nearest cent)

After 5 interest payments, Bob will have approximately $127.63 in his savings account.