Question

How much should you be willing to pay for an annuity that will provide $300 every 3 months for 6 years starting 3 months from now if you want to make a nominal 12% per year compounded quarterly? Another words, what is the present worth of the benefit that is described here? Also,draw a properly labeled Cash Flow Diagram for this question.

Answer 1

Given

Quarter	Cash flow
1	300
2	300
3	300
4	300
5	300
6	300
7	300
8	300
9	300
10	300
11	300
12	300
13	300
14	300
15	300
16	300
17	300
18	300
19	300
20	300
21	300
22	300
23	300
24	300

Quarterly Payment A=$300

Interest Rate =12%

Quarterly interest rate r=12%/4=3%

Number of Quarters in 6 years N=24 quarters

Present Value PV =A*(1-(1+r)^-N)/r

PV=300*(1-(1+3%)^-24)/3%

PV=$5080.66