On his 12th birthday Enoch's grandparent's deposited $25 into a savings account for him. Each month after that up to and including his 20th birthday, they deposit $10 more than the previous month. How much money will Enoch have on his 20th birthday, excluding interest?
I got $48,000, am I right?
96 months would be up to his 20th birthday, so it is 97 months as that is including his 20th birthday.
So the solution would be:
S97= 97/2 • [2(25) + (97-1)(10)]
S97=$48 985
To determine the total amount of money Enoch will have on his 20th birthday, we need to calculate the total sum of all the monthly deposits starting from his 12th birthday.
First, let's calculate how many monthly deposits there will be from his 12th birthday to his 20th birthday. Since his 12th birthday counts as the starting point, there are 8 years between his 12th and 20th birthdays.
Since there are 12 months in a year, we multiply 8 years by 12 months: 8 years × 12 months/year = 96 months.
Now, let's determine the monthly deposit amounts. We know that his grandparents deposited $25 on his 12th birthday, and each subsequent month they increase the deposit amount by $10.
To find the monthly deposit amounts, we need to create a sequence in which each term is derived by adding $10 to the previous term.
12th birthday deposit: $25
13th birthday deposit: $25 + $10 = $35
14th birthday deposit: $35 + $10 = $45
15th birthday deposit: $45 + $10 = $55
…
20th birthday deposit: $25 + 9 × $10 = $25 + $90 = $115.
Now that we have established the sequence of monthly deposit amounts, we can calculate the sum of these amounts for the 96 months:
Sum = (number of terms / 2) × (first term + last term)
= (96 / 2) × ($25 + $115)
= 48 × $140
= $6,720.
Therefore, Enoch will have $6,720 in his savings account on his 20th birthday, excluding interest.
So your calculation of $48,000 is incorrect.
To solve this question, we need to determine the total amount of money that Enoch's grandparents deposit into his savings account from his 12th birthday to his 20th birthday.
Let's break down the given information:
- On his 12th birthday, Enoch's grandparents deposited $25.
- Each month after that up to and including his 20th birthday, they deposit $10 more than the previous month.
To find the total amount of money deposited, we can create a sequence:
25, (25 + 10), (25 + 10 + 10), ..., (25 + 10(n-1))
To calculate the nth term of this sequence, we can use the formula:
An = A1 + (n-1)d
Where An represents the nth term, A1 is the first term, n is the number of terms, and d is the common difference.
In this case, A1 = 25, d = 10, and n = 20 - 12 + 1 = 9.
Calculating the 9th term:
A9 = 25 + (9-1) * 10
A9 = 25 + 8 * 10
A9 = 25 + 80
A9 = 105
Finally, we need to find the sum of all terms from the 1st term to the 9th term. We can use the sum formula for an arithmetic sequence to find the total amount deposited:
Sn = (n/2)(A1 + An)
Substituting the values into the formula:
S9 = (9/2)(25 + 105)
S9 = (9/2)(130)
S9 = 585
Therefore, Enoch will have a total of $585 deposited into his savings account by his 20th birthday, excluding interest.