Question

11. What is the present value of a 10-year annuity with annual payments of 50 and an interest rate of 5?
a. Do this with your calculator, indicating what number you put in each button.
b. Do this in Excel, using the annuity formula.
12. What is the present value of a cash flow of 1000 being paid in 10 years with an interest rate of 5%?
13. What is the sum of the calculations in (11) and (12)? What is another way to describe this sum?

Answer 1

First question is being answered here:

(a) Here, the payments will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $50, r is the rate of interest =5% and n is the time period = 10

Now, putting these values in the above formula, we get,

PVA = $50 * (1 - (1 + 5%)-10 / 5%)

PVA = $50 * (1 - ( 1+ 0.05)-10 / 0.05)

PVA = $50 * (1 - ( 1.05)-10 / 0.05)

PVA = $50 * (1 - 0.61391325354) / 0.05)

PVA = $50 * (0.38608674646 / 0.05)

PVA = $386.09

So, present value of cash flows = $386.09

(b) Using excel, we will use the following formula to calculate the required present value:

=PV(5%,10,-50)

Above formula will give the result of $386.09