Find the present value of an ordinary annuity of $600 payments each made quarterly over 5 years and earning interest at 4% per year compounded quarterly.
quarterly rate = .04/4 = .01
number of payments = 5(4) = 20
PV = payment (1 - (1+i)^-n)/i
600( 1 - 1.01^-20 )/.01
= $10837.33
To find the present value of an ordinary annuity, we need to use the formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV is the present value of the annuity,
PMT is the payment made at each period,
r is the interest rate per period, and
n is the total number of periods.
Given:
PMT = $600 (quarterly payments)
r = 4% per year (compounded quarterly)
n = 5 years (20 quarters)
First, we need to adjust the interest rate to match the compounding period. Since the interest rate is given per year but compounded quarterly, we divide the annual interest rate by 4 to get the quarterly interest rate:
r = 4% / 4 = 1% = 0.01 (as a decimal)
Next, we substitute the values into the formula:
PV = $600 * [(1 - (1 + 0.01)^(-20)) / 0.01]
Now, let's calculate the present value of the annuity:
PV = $600 * [(1 - (1.01)^(-20)) / 0.01]
PV = $600 * [(1 - 0.8179) / 0.01]
PV = $600 * (0.1821 / 0.01)
PV = $600 * 18.21
PV = $10,926
Therefore, the present value of an ordinary annuity of $600 payments each made quarterly over 5 years and earning interest at 4% per year compounded quarterly is $10,926.