Final answer:
Jeff is planning to save for his retirement using an ordinary annuity, but without a specified interest rate, we cannot calculate his retirement account balance. The formula for such a calculation involves the future value of an annuity formula. Starting early and utilizing the power of compound interest is vital for growth over time.
Step-by-step explanation:
To calculate how much money Jeff will have in his retirement account, we need to consider that the savings constitute an annuity, which is a series of equal payments made at regular intervals. The formula for the future value of an annuity where deposits are made at the end of each period (also known as an ordinary annuity) is:
FV = P * [(1 + r)^n - 1] / r
where:
FV is the future value of the annuity.
P is the payment amount per period.
r is the interest rate per period.
n is the total number of payments.
In Jeff's case, the payment (P) is $116, but we do not have the interest rate (r) or the total number of payments (n). Assuming there is a positive interest rate but without knowing what it is, we cannot provide the exact future value. However, we know he will make these payments every year for 15 years, following which the amount will continue to compounded annually for another 10 years until his retirement.
If we had the interest rate, we could calculate the amount deposited over 15 years and then apply compound interest on the accumulated sum for the remaining 10 years until his retirement. The importance of starting early with savings and allowing compound interest to work over time can be shown in the examples given, where even small savings can grow significantly.
Without the interest rate, we are boxed in when it comes to providing a numeric answer, but it's certain that thanks to the power of compound interest, the earlier and longer one saves, the more substantial the retirement fund becomes. Moreover, given a positive interest rate, it's safe to say that Jeff's total retirement savings would be more than the sum of his individual deposits, highlighting the benefit of compound interest over time.