Mike started a savings account by depositing $9. Each month, he deposits more money than the month before. At the end of 41 months, he has saved $9,389.00. How much more does he deposit each month?
it 11
To find out how much more money Mike deposits each month, we can set up an equation using the given information.
Let's represent the amount of money Mike deposits each month as 'x'.
In the first month, Mike deposits $9.
In the second month, he deposits $9 + x.
In the third month, he deposits $9 + (2x).
This pattern continues, and at the end of 41 months, he has saved $9,389.
Therefore, the equation can be written as:
9 + (9 + x) + (9 + 2x) + ... + (9 + 40x) = 9,389
To solve this equation, we can use the formula for the sum of an arithmetic series:
S = (n/2) * (2a + (n-1)d)
Where:
S = sum of the series,
n = number of terms,
a = first term,
d = common difference.
In this case, we have:
S = 9,389,
n = 41,
a = 9,
d = x.
Plugging in these values into the formula, we have:
9,389 = (41/2) * (2*9 + (41-1)x)
Simplifying further:
9,389 = 20.5 * (18 + 40x)
Dividing both sides by 20.5:
(9,389 / 20.5) = 18 + 40x
457.7073 = 18 + 40x
Subtracting 18 from both sides:
439.7073 = 40x
Finally, dividing by 40:
x ≈ 10.9937
Therefore, Mike deposits approximately $10.99 more each month.
To find out how much more Mike deposits each month, we need to determine the difference between the deposits made in consecutive months.
Let's break down the problem step by step:
1. Start with the initial deposit: $9.
2. Assume that Mike deposits x additional dollars each month.
3. To find out how much he deposits in the second month, we add his initial deposit and the additional amount: $9 + x.
4. In the third month, he will deposit his initial deposit, the additional amount, and another x dollars: $9 + x + x = $9 + 2x.
5. Continuing this pattern, after 41 months, he will have deposited: $9 + (x + x + x + ... 41 times) = $9 + 41x.
6. According to the problem, the total savings after 41 months is $9,389. So we can set up the equation: $9 + 41x = $9,389.
7. To isolate the x term, we subtract $9 from both sides of the equation: 41x = $9,389 - $9.
8. Simplify: 41x = $9,380.
9. Finally, we solve for x by dividing both sides of the equation by 41: x ≈ $228.54.
Therefore, Mike deposits approximately $228.54 more each month compared to the previous month.
All kinds of missing information:
- how much more each month does he deposit ?
- are the increases each month the same amount?
- does he not get any interest in his savings account? (if not, he might as well put each month's deposit in a sock under his bed, at least he won't get hit with any service charges )