Final answer:
To determine the annual deposit needed to retire with $210,000 at an annual interest rate of 10.5%, the future value annuity formula is used. The calculation involves using the values of a 10.5% interest rate, a 36-year investment period, and the desired future value of $210,000, to solve for the payment amount.
Step-by-step explanation:
The question involves finding out how much a 28-year-old individual needs to deposit annually into her retirement account, with a 10.5% annual interest rate, to accumulate $210,000 by the age of 65. This calculation requires the use of the formula for the future value of an annuity. The formula we'll use is PV = PMT * [(1 - (1 + r)^(-n)) / r], where PV is the present value (or the amount needed today), PMT is the annual payment, r is the interest rate, and n is the number of payments.
To solve for PMT, we rearrange the formula: PMT = PV / [(1 - (1 + r)^(-n)) / r]. In this case, PV (future value desired) is $210,000, r (annual interest rate) is 10.5% or 0.105, and n (number of payments) is 65 - 28 - 1 = 36 (since the last deposit will be made at retirement and not a year after).
By substituting the values into the formula we get PMT = 210,000 / [(1 - (1 + 0.105)^(-36)) / 0.105], which when calculated gives the annual deposit required for the retirement account. The exact figure should be rounded to two decimal places.