Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) Find the present value of the ordinary annuity. (Round your answer to the nearest cent.)

Question

Find the present value of the ordinary annuity. (Round your answer to the nearest cent.)

$1100/semiannual period for 6 years at 4%/year compounded semiannually.



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Answer 1

The key to solving this type of problem is understanding what each part of the formula represents. The formula is:

PV = C { [ 1 - (1+i)^-n ] ⁄ i } (1 + i)

C = amount paid each period

r = the annual interest rate

p = # of periods per year

i = r ⁄ p

n = # of periods = [(# of years) * p]

(notice the exponent is "- n")

As you can see in the list if variables above I included r and p, even though they are not in the equation. This is because you need to know them to get the correct values of i and n.

So in your problem,

C = $1100

r = 4% = 0.04

p = 2 (semiannually means twice per year)

i = 0.04 ⁄ 2 = 0.02

n = 6 * 2 = 12

PV = ($1100) * { [ 1 - (1.02)^-n ] ⁄ (0.02) } * (1.02) = $11,865.53