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Cassandra receives an annuity-due with a payment each month. The annuity has its first payment on her 12th birthday and the last payment is on her 16th birthday. The amount of the payment is $100 times her age with no credit being given for fractions of a year. A the deposits are made to an account earning compound interest at an annual effective interest rate of 5.63%. Find the accumulated value on her 18th birthday. (Round your answer to the nearest cent.)

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Answer:

To find the accumulated value on Cassandra's 18th birthday, we first need to calculate the total amount of deposits made into the account over the 6-year period, from her 12th to her 16th birthday.

Since the annuity has a payment each month, Cassandra will make a total of 12 payments each year, from her 12th to her 16th birthday. The amount of each payment is $100 times her age.

Let's calculate the total deposits:

12 payments/year * $100 * 12 years = $14,400

Therefore, Cassandra will make a total of $14,400 in deposits into the account.

Now, we need to calculate the accumulated value of these deposits at an annual effective interest rate of 5.63% over a 2-year period, from Cassandra's 16th to her 18th birthday.

To calculate the accumulated value, we use the formula: A = P(1 + r/n)^(nt)

Where:

A is the accumulated value

P is the principal amount (deposits made)

r is the annual interest rate

n is the number of times the interest is compounded per year

t is the number of years

In this case, the deposits are made monthly, so n = 12 (monthly compounding), r = 5.63% = 0.0563, and t = 2 years.

Using the formula, we can calculate the accumulated value:

A = $14,400 * (1 + 0.0563/12)^(12*2)

Calculating this expression, we find that the accumulated value on Cassandra's 18th birthday is approximately $15,828.62.

Therefore, rounded to the nearest cent, the accumulated value on her 18th birthday is $15,828.62.

User Ayoub Kaanich
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