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.