Question

Your uncle is giving you $250 every year for the next ten years. There are two choices for using the money: you may either save the money with a bank which pays you an interest of 4% per year or invest the money with a bond paying you annul interest of 6%. a. what is the discount rate for you to find the present value? b. what is the value in present value if you are receiving the money at the end of each year? c. what is the value in present value if you are receiving the money at the beginning of each year? d. What is the difference between the answers in parts (b) and (c) and why will there be such a difference?

Answer 1

Given: Annuity = $250, Period = 10 years, There are 2 choices

Choice 1 = 4% interest in Saving Banl Account

Choice 2 = 6% Annual interest in Bond

a) What is the discount rate for yiu to find the present value?

From above two options Investing in bond provides more return 6% than bank 5%. So we will go with investing in bond. So aordingly our required rate of return is 6% whihc will become the discounting rate to find the present value.

b) Presnt value if Year end Payments:

PV = Annuity x cumulative discounting factor @ 6% for 10 years.

[ For Cumulative discount/pv factor refer the table or can calculate as it is sum of (100/106) + (100/106)² ...............(100/106)¹⁰ ]  

= 250 x 7.360087015

Present value = 1840.021753

c) Present value if Beginning of year payment

PV = Annuity + Annuity x cumulative discounting factor @ 6% for 9 years.

[ For Cumulative discount/pv factor refer the table or can calculate as it is sum of (100/106) + (100/106)² ...............(100/106)⁹ ]  

= 250 + 250 x 6.801692244

= 250 + 1700.423061

Present value = 1950.423061

d)

As you notice Amount in (c) is 110.401308 higher then value in point (b). This because the discounting effect. In (b) payments are due at the end of year so 1st payment due at end of 1st year but in (c) payments are due beginning of the year so 1st payment due today. and this makes discounting lesser for 1 payment. The payment due today doen't need to discount. In (b) all payments are discounted to get pv but in (c) payments shift 1 year earlier and 9 payments are discounted. So for this time value of money (c) getts higher pv.