Question

What is the present value of a 6-yr annuity with annual payments of $1,012, paid at the beginning of each year, and evaluated at a 10.5 percent interest rate, which is compounded quarterly? Please show financial calculator key strokes.

Answer 1

Here, the cash inflow will be same every year, so it is an annuity. And since the cash flows will start at the beginning of each year so it will be termed as an annuity due. For calculating the present value of annuity due, we will use the following formula:

PVAD = P * (1 - (1 / (1 + r)ⁿ / r) * (1 + r)

where, PVD is the present value of annuity due, P is the periodical amount = $1012, r is the rate of interest = 10.5% compounded quarterly. So quarterly rate = 10.5% / 4 = 2.625% and n is the time period = 6 * 4 = 24.

Now, putting these values in the above formula, we get,

PVAD = $1012 * (1 - (1 / (1 + 2.625%)²⁴ / 2.625%) * (1 + 2.625%)

PVAD = $1012 * (1 - (1 / (1 + 0.02625)²⁴ / 0.02625) * (1 + 0.02625)

PVAD = $1012 * (1 - (1 / (1.02625)²⁴ / 0.02625) * (1.02625)

PVAD = $1012 * (1 - (1 / 1.86241338004) / 0.02625) * (1.02625)

PVAD = $1012 * (1 - 0.536937723234421) / 0.02625) * (1.02625)

PVAD = $1012 * (0.463062276765579 / 0.02625) * (1.02625)

PVAD = $1012 * (17.64046768630777) * (1.02625)

PVAD = $18320.77