Question

A company has set up an a annuity will that will pay $44,000.00 at the beginning of every six months for 5.5 years. If the annuity pays 4.4%, compounded semi-annual. What amount was invested for this annuity?

The amount invested was $_____. (Round to 2 decimal places.)

Answer 1

Annuity pays $44,000 at the beginning of every 6 months for the next 5.5 years.
So first $44,000 is received at the initial moment itself. Let's take it separately as no interest will be accrued on it.

So now we get $44,000 at the end of every 6 months for the next 5 years (excluding the first $44,000)

P = A[ (1+r)ⁿ -1] / [ r (1+r)ⁿ] where r = 4.4% / 2 = 2.2% (since 4.4% is compounded semi-annually)
n = number of terms = 5*2 = 10 ; A = Annuity and P = principal

P = 44000 [ (1+0.022)¹⁰ -1] / [0.022 (1.022)¹⁰ ]

P = 44000 (0.2431) / (0.022 * 1.2431) = 10696.4 / 0.0273482 = 391118.976

To this principal sum, add $44,000 that you would get initially.

Thus, the amount invested = 391118.976 + 44000 = 435118.976 = $435,118.98