Future and Present Value of an Annuity Due If you start making $25 monthly contributions today and continue them for four years,what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?
A)$101.26, $99.26
B)$1,352.45, $1,064.51
C)$1,359.21, $1,069.83
D)$2,171.02, $1,516.03

Question

Quizplus · Accepted Answer

To calculate the future value of the annuity due, we need to use the formula:

FV = Pmt x [(1 + r) x ((1 + r)^n - 1) / r]

where:

Pmt = $25 (the monthly contribution)
r = 6% / 12 = 0.005 (the monthly interest rate)
n = 4 x 12 = 48 (the total number of monthly contributions)

Plugging in the numbers gives us:

FV = $25 x [(1 + 0.005) x ((1 + 0.005)^48 - 1) / 0.005] = $1,359.21

To calculate the present value of the annuity, we can use the formula:

PV = Pmt x [(1 - (1 + r)^-n) / r] x (1 + r)

Plugging in the numbers gives us:

PV = $25 x [(1 - (1 + 0.005)^-48) / 0.005] x (1 + 0.005) = $1,069.83

Therefore, the best choice is C, as it matches both the future value and present value calculations.

Future and Present Value of an Annuity Due If You