Question

olly purchases a retirement annuity that will pay her $2,500 at the end of every six months for the first twelve years and $300 at the end of every month for the next five years. The annuity earns interest at a rate of 4.3% compounded quarterly.

a. What was the purchase price of the annuity?

Round to the nearest cent

b. How much interest did Holly receive from the annuity?

Round to the nearest cent

Answer 1

Answer (a):

The annuity is for (12 + 5 =) 17 years.

(i) First let us calculate the value of annuty at the start of year 13 (of retirement):

Effective annual interest = (1 + 4.3%/4)^4 - 1 = 4.3698357542%

Monthly interest = (1 + 4.3698357542)^(1/12) - 1 = 0.357056920%

Present value of annuity at start of Year 13 = PV (rate, nper, pmt, fv, type) = PV (0.35705692%, 5*12, -300, 0, 0)

= $16,176.63

(ii)

Now let us calculate calculate the PV of annuity at the start of retirement:

Semiannual interest = (1 + 4.3%/4) ^2 -1 =2.16155625%

PV of annuity at the start of retirement = PV (rate, nper, pmt, fv, type)

= PV (2.16155625%, 12*2, -2500, -16176.63, 0)

= $56113.25

Purchase price of the annuity = $56,113.25

Answer (b):

Interest Holly received from annuity = Sum of all annuty amounts - Purchase price of annuity

= (2500 * 12 * 2 + 300 * 12 * 5) - 56113.25

= $21886.75

Interest Holly received from annuity = $21,886.75