Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in additional 10% of the amount in the account each week.
1)Who has more money after the first additional deposit? Explain.
2)Who has more money after the second additional deposit? Explain.
3)How do you think the amount in the two accounts will compare after a month? A year?
THANK YOU!!!
Leroy will NEVER have more.
Question
Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in an additional 10% of the amount in the account each week.
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To find the answers to these questions, we can calculate the amount of money in each person's account after each additional deposit.
1) To find out who has more money after the first additional deposit, we need to calculate the amount in each person's account after that deposit.
Leroi's additional deposit: $10
Sylvia's additional deposit: 10% of the current amount in the account
After the first additional deposit:
- Leroi's total amount = $100 + $10 = $110
- Sylvia's total amount = $100 + (10% of $100) = $100 + $10 = $110
Both Leroi and Sylvia will have the same amount of money after the first additional deposit, which is $110. So they will have the same amount of money.
2) To find out who has more money after the second additional deposit, we again need to calculate the amount in each person's account after that deposit.
Leroi's additional deposit: $10
Sylvia's additional deposit: 10% of the current amount in the account
After the second additional deposit:
- Leroi's total amount = $110 + $10 = $120
- Sylvia's total amount = $110 + (10% of $110) = $110 + $11 = $121
After the second additional deposit, Sylvia will have more money in her account with $121, compared to Leroi's $120. This is because Sylvia's additional deposit is calculated based on the current amount in her account, while Leroi consistently adds the same amount every week.
3) After a month or a year, the amount in the two accounts will depend on the number of weeks in that period. Assuming a month has four weeks and a year has 52 weeks:
After a month:
- Leroi's total amount = $100 + ($10 * 4) = $140
- Sylvia's total amount = $100 + (10% of $100 * 4) = $100 + ($10 * 4) = $140
Both Leroi and Sylvia will have the same amount, which is $140 after a month.
After a year:
- Leroi's total amount = $100 + ($10 * 52) = $700
- Sylvia's total amount = $100 + (10% of $100 * 52) = $100 + ($10 * 52) = $700
Again, both Leroi and Sylvia will have the same amount, which is $700 after a year. This is because with Sylvia's 10% additional deposit, the amount in her account also increases over time.
Overall, after each additional deposit, Leroi and Sylvia will have the same amount in their accounts if the number of weeks is the same.
1. Neither. 10% of $100 = $10
2. 10% of $110 = $11
3. Leroi will have more.