Question

Through Buzz under the assignment.

1. lan deposits $2,400 each quarter for 3 years. The annuity earns 10% interest and is compounded quarterly. Find the present value of the annuity.
Using the Present Value of Ordinary Annuity Table, the correct factor for 12 compounding periods at 2.5% interest is 10.25776.

Answer 1

$56,577.12

Explanation:

To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:

PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)

Where:

PV = present value

PMT = payment amount per compounding period

r = annual interest rate

n = number of compounding periods per year

t = total number of years

Plugging in the given values, we get:

PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)

PV = 2400 x [1 - (1.025)^(-12)] / (0.025)

PV = 2400 x [1 - 0.610355] / 0.025

PV = 2400 x 23.5742

PV = $56,577.12 (rounded to the nearest cent)

Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.