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?

Question

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?

Answer 1

P = Po(1+r)^n

P = 100(1+0.05)^5
P = 100(1.05)^5 = $127.63.

Answer 2

To answer this question, we need to calculate the interest Bob will earn each year and add it to his original deposit.

Step 1: Calculate the interest earned in the first year.
Bob's initial deposit is $100. The bank pays him 5% interest on this amount. To find the interest earned, we can use the formula:

Interest = Principal * Interest Rate

In this case, the principal is $100 and the interest rate is 5%. Substituting the values into the formula:

Interest = $100 * 0.05 = $5

So, Bob earns $5 in interest in the first year.

Step 2: Add the interest earned to the principal.
Bob's total savings at the end of the first year will be:

Total savings = Principal + Interest = $100 + $5 = $105

Step 3: Repeat steps 1 and 2 for the subsequent years.
Since Bob will earn 5% interest at the end of each year, we'll calculate the interest earned and add it to his total savings for the remaining 4 years.

Year 2:
Interest = $105 * 0.05 = $5.25
Total savings = $105 + $5.25 = $110.25

Year 3:
Interest = $110.25 * 0.05 = $5.51
Total savings = $110.25 + $5.51 = $115.76

Year 4:
Interest = $115.76 * 0.05 = $5.79
Total savings = $115.76 + $5.79 = $121.55

Year 5:
Interest = $121.55 * 0.05 = $6.08
Total savings = $121.55 + $6.08 = $127.63

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

Answer 3

To calculate Bob's savings account balance after 5 interest payments, we need to calculate the interest for each year and add it to the previous balance.

Step 1: Calculate the interest for each year.
Year 1 interest: $100 * 5% = $5
Year 2 interest: ($100 + $5) * 5% = $5.25
Year 3 interest: ($105 + $5.25) * 5% = $5.75
Year 4 interest: ($110.25 + $5.75) * 5% = $5.82
Year 5 interest: ($116 + $5.82) * 5% = $6.08

Step 2: Add the interest to the previous balance.
Savings account balance after 5 years: $100 + $5 + $5.25 + $5.75 + $5.82 + $6.08 = $128.90

Therefore, Bob will have approximately $128.90 in his savings account after 5 interest payments.