In June, Cory beings to save money for a video game and a TV he wants to buy in December. He starts with $22. Each month he plans to save 10% more than the previous math. How much money will he have at the end of December?
In July, Cory saves 10% more than $22, which is $2.20. So he has saved a total of $24.20 (22+2.20) by the end of July.
In August, Cory saves 10% more than $24.20, which is $2.42. So he has saved a total of $26.62 (24.20+2.42) by the end of August.
Cory continues saving 10% more than the previous month's savings each month until December.
By the end of September, Cory has saved $29.28.
By the end of October, Cory has saved $32.21.
By the end of November, Cory has saved $35.43.
Finally, by the end of December, Cory has saved a total of $38.97. This is the amount he will have to buy his video game and TV.
are you sure
Yes, the calculations are correct. Here's a breakdown:
- June: Cory saves $0, starting with $22
- July: Cory saves 10% more than $22, which is $2.20. He has a total of $24.20.
- August: Cory saves 10% more than $24.20, which is $2.42. He has a total of $26.62.
- September: Cory saves 10% more than $26.62, which is $2.66. He has a total of $29.28.
- October: Cory saves 10% more than $29.28, which is $2.93. He has a total of $32.21.
- November: Cory saves 10% more than $32.21, which is $3.22. He has a total of $35.43.
- December: Cory saves 10% more than $35.43, which is $3.54. He has a total of $38.97.
Therefore, Cory will have saved $38.97 by the end of December.
To calculate how much money Cory will have at the end of December, we need to calculate his savings for each month and then add them up.
Given:
Starting amount = $22
Increase in savings every month = 10%
Let's calculate his savings for each month:
Month 1:
Starting amount = $22
Savings for month 1 = starting amount = $22
Month 2:
Starting amount = $22
Increase in savings = 10% of starting amount = 10% of $22 = $2.20
Savings for month 2 = starting amount + increase in savings = $22 + $2.20 = $24.20
Month 3:
Starting amount = $24.20
Increase in savings = 10% of starting amount = 10% of $24.20 = $2.42
Savings for month 3 = starting amount + increase in savings = $24.20 + $2.42 = $26.62
Month 4:
Starting amount = $26.62
Increase in savings = 10% of starting amount = 10% of $26.62 = $2.66
Savings for month 4 = starting amount + increase in savings = $26.62 + $2.66 = $29.28
Month 5:
Starting amount = $29.28
Increase in savings = 10% of starting amount = 10% of $29.28 = $2.93
Savings for month 5 = starting amount + increase in savings = $29.28 + $2.93 = $32.21
Month 6:
Starting amount = $32.21
Increase in savings = 10% of starting amount = 10% of $32.21 = $3.22
Savings for month 6 = starting amount + increase in savings = $32.21 + $3.22 = $35.43
Month 7:
Starting amount = $35.43
Increase in savings = 10% of starting amount = 10% of $35.43 = $3.54
Savings for month 7 = starting amount + increase in savings = $35.43 + $3.54 = $38.97
Month 8:
Starting amount = $38.97
Increase in savings = 10% of starting amount = 10% of $38.97 = $3.90
Savings for month 8 = starting amount + increase in savings = $38.97 + $3.90 = $42.87
Month 9:
Starting amount = $42.87
Increase in savings = 10% of starting amount = 10% of $42.87 = $4.29
Savings for month 9 = starting amount + increase in savings = $42.87 + $4.29 = $47.16
Month 10:
Starting amount = $47.16
Increase in savings = 10% of starting amount = 10% of $47.16 = $4.72
Savings for month 10 = starting amount + increase in savings = $47.16 + $4.72 = $51.88
Month 11:
Starting amount = $51.88
Increase in savings = 10% of starting amount = 10% of $51.88 = $5.19
Savings for month 11 = starting amount + increase in savings = $51.88 + $5.19 = $57.07
Month 12:
Starting amount = $57.07
Increase in savings = 10% of starting amount = 10% of $57.07 = $5.71
Savings for month 12 = starting amount + increase in savings = $57.07 + $5.71 = $62.78
To find out the total savings at the end of December, we add up the savings for each month:
Total savings = Sum of savings for each month
= $22 + $24.20 + $26.62 + $29.28 + $32.21 + $35.43 + $38.97 + $42.87 + $47.16 + $51.88 + $57.07 + $62.78
= $477.37
Therefore, Cory will have $477.37 at the end of December.