Final answer:
The annual effective interest rate (i) for Ms. Kitty's savings account can be found by setting up an equality between the future values of both Ms. Kitty's and Mr. Puppy's accounts and solving for i using the formula for the future value of an annuity.
Step-by-step explanation:
The question involves finding the annual effective interest rate (i) for Ms. Kitty's savings account, given that the future value of both Ms. Kitty's and Mr. Puppy's accounts are the same after n years, with different interest rate profiles and series of deposits.
To solve for the annual effective interest rate (i), we must use the formula for the future value of an annuity. The future value (FV) of an annuity is calculated as:
FV = PMT × ((1 + i)^n - 1) / i
where PMT is the periodic payment (500 in this case), i is the effective interest rate, and n is the number of periods.
Since both Kitty's and Puppy's funds have accumulated to 11965.51515 after n years, and we know the interest scenarios for Mr. Puppy's account, we can establish an equation based on the annuity's future value and solve for i, the interest rate for Ms. Kitty’s account.
It is important to note that the actual calculation requires careful handling of the variable n, and a sequence of calculations to establish the equality between Ms. Kitty's and Mr. Puppy’s future values while considering their different interest rate periods. Due to the complexity of the calculations, they might not be easily achieved without the aid of a financial calculator or appropriate software.
Understanding the concept of compound interest is essential, as it is the key to calculating the future worth of investments, as seen in the referenced information where the original investment grows at a rate compounded over time.