Sapna’s grandparents deposit $1200 into a college savings account on her 5 thbirthday. They continue to make this birthday deposit each year until making the ﬁnal deposit on her 18 th birthday. If the account earns 5% interest annually, how much is there after the ﬁnal deposit?

Question

Sapna’s grandparents deposit $1200 into a college savings account on her 5 thbirthday. They continue to make this birthday deposit each year until making the ﬁnal deposit on her 18 th birthday. If the account earns 5% interest annually, how much is there after the ﬁnal deposit?

Answer 1

To calculate the amount in the college savings account after the final deposit, we can break down the problem into smaller steps.

Step 1: Calculate the annual interest earned on each deposit.
The account earns 5% interest annually, so for each deposit, we can calculate the interest by multiplying the deposit amount by 5%:
Interest = Deposit Amount * 5%

Step 2: Calculate the total value of each deposit after earning interest.
By adding the original deposit and the interest earned, we can calculate the total value of each deposit:
Total Value = Deposit Amount + Interest Earned

Step 3: Calculate the total value of all deposits made.
Since Sapna's grandparents make the same deposit on her birthday each year, we need to calculate the total value of all deposits made over the years. Assuming Sapna's birthday is on the same day each year, we can use the formula for the sum of an arithmetic series:
Total Value of All Deposits = (Number of Years) * ((First Deposit + Last Deposit) / 2)

Step 4: Calculate the final value after the last deposit.
To find the final value after the last deposit, we add the total value of all deposits made to the original deposit amount on Sapna's 18th birthday.

Let's calculate each step:

Step 1: Calculate the annual interest earned on each deposit.
Interest = $1200 * 5% = $60

Step 2: Calculate the total value of each deposit after earning interest.
Total Value = $1200 + $60 = $1260

Step 3: Calculate the total value of all deposits made.
In this case, the deposits are made for 14 years (from the 5th birthday to the 18th birthday):
Total Value of All Deposits = 14 * (($1200 + $1200) / 2) = $14,400

Step 4: Calculate the final value after the last deposit.
To find the final value, we add the total value of all deposits to the original deposit amount on Sapna's 18th birthday:
Final Value = $14,400 + $1200 = $15,600

Therefore, the amount in the college savings account after the final deposit is $15,600.