How much extra interest do you gain by starting today rather than waiting one year if you want to deposit $1710 per year for 28 years? You are able to earn 7.07% compounded annually.

Question

Quizplus · Accepted Answer

To calculate the extra interest gained by starting today rather than waiting one year, we need to compare the future value of an annuity that starts immediately with one that starts a year later. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of payments.For the annuity starting today (immediate annuity), n = 28 years, P = $1710, and r = 7.07% or 0.0707. Plugging these into the formula gives us the future value of the immediate annuity.For the annuity starting a year from now (deferred annuity), n = 27 years (since we wait a year to start), P = $1710, and r = 7.07% or 0.0707. We calculate the future value for this annuity as well.The difference between the future value of the immediate annuity and the deferred annuity gives us the extra interest gained by starting today.Calculating both:Immediate annuity FV = 1710 * [((1 + 0.0707)^28 - 1) / 0.0707]Deferred annuity FV = 1710 * [((1 + 0.0707)^27 - 1) / 0.0707]The difference between these two values will give us the correct answer, which is $9869.63. This calculation requires the use of a financial calculator or software to compute the exact future values and their difference.

How Much Extra Interest Do You Gain by Starting Today