Question

How much would you have to invest today in the bank at an interest rate of 8% to have an annuity of 7,000 per year for 8 years, with nothing left in the bank at the end of the 8 years? Select the amount below that is closest to your answer. Ignore income taxes) Use the selections from the present value tables below! Present Value of $1 Period % 8\% 4 0.855 0.681 8 0.540 16 0534 0.292 Present Value of an Annuity of $1 Period % 3.630 3.312 6.733 5.747 11.652 8.851 All answers are rounded to the nearest . A $ 3,780 B. $ 2,044 40,229

Answer 1

Correct Option is C $40229

1) It can be find directly by Finding Present value of Cash Flow

PV of cash flows = Annual Cash Flow * PVF(8%for 8 yr )

PV of Cash flow = 7000* PVAF (8%,8yr )

=7000*5.747

=40229

Present value of annuity factor for 8 year is taken instead of Present value factor as the annual cash flows are equal

or by Present Value of Annuity formula

2) The Annuity per year can be find by the Present Value Annuity Factor that will give future annual Cash inflow

Formula fro PV of Annuity (P)= A [1-(1+r)-n] / r or A [1-(1/(1+r)n ] /r

Where A is Annual payment or Receipt

r is Rate of interest

n isnumber of year

P= 7000[1-(1/1+0.08)8/0.08]

=7000[1-0.5403/0.08

=7000[0.4597/0.08]

=7000*5.7463

=40224.1 approx ans to 40229 as we have taken PVF for 8% which is rounded off