Related to Checkpoint 6.2) (Present value of an ordinary annuity) Nicki Johnson,
ID: 2809837 • Letter: R
Question
Related to Checkpoint 6.2) (Present value of an ordinary annuity) Nicki Johnson, a sophomore mechanical engineering student, receives a call from an insurance agent who believes that Nicki is an older woman who is ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her a fixed annual income. The annuities are as follows Annuity 8 Purchase Price of the Annuity (At t 0) $60,000 $50,000 $50,000 Amount of Money Received Per Year $9,000 $%7,000 $6,500 Duration of the Annuity (Years) 25 18 Nicki could eam 11 percent on her money by placing it in a savings account. Alternatively, she could place it in any of the above annuities. Which annuities in the table above, if any. will ean Nicki a higher retum than investing in the savings account eaning 11 percent? a. If Nicki could earn 11 percent on her money, what is the present value of annuity A with $9,000 payments per year and 22 years duration? $(Round to the nearest cent.)Explanation / Answer
Present value of annuity can be computed as:
PV = C x PVIFA (i, n)
C is periodic cash flow, i is the rate of return and n is the no. of periods
PV of annuity A = $ 9,000 x PVIFA (11 %, 22)
= $ 9,000 x 8.1757 = $ 73,581.30
PV of annuity B = $ 7,000 x PVIFA (11 %, 25)
= $7,000 x 8.4217 = $ 58,951.90
PV of annuity C = $ 6,500 x PVIFA (11 %, 18)
= $ 6,500 x 7.7016 = $ 50,060.40
Annuity stream A gives higher return than other two, as computed PV of $ 73,581.30 at 11% rate is higher than the initial investment in Annuity stream A.
Of course investment in Annuity B, $ 50,000 is less than estimated PV of $ 58,951.90, but the difference between estimated and investment in case of annuity A is more than that of B.
Annuity A will give Nicki higher return than 11%.