Question

Suppose that you just paid $76,000 for a security that will make its first payment to you in 7 years from today. It will continue to make equal annual payments every year indefinitely. Find the size of the payments that you will receive from the security if the interest rate is 5%

Answer 1

Answer:

$5,346.98

Explanation:

Initial cash flow = 76,000

Discount rate = 5%

Suppose the C.F. in the 7th year is x which will flow till perpetuity

Present value of annual cash flow till perpetuity = Annual cash flow / Discount rate

PV at the 7th year = x/0.05

Discount factor = (1 + r)^n

Discount rate = 5%

Years   D. factor   Cash flows

0                 0            76,000

1           0.952381            -

2          0.907029           -

3          0.863838           -

4          0.822702           -

5          0.783526           -

6          0.746215            -

7           0.710681          x/0.05

So, 76000 = 0.710681 *(x/0.05)

76000 / 0.710681  = x / 0.05

x = 76000 / 0.710681 * 0.05

x = 5346.98408990813

x = 5346.98

Hence, if the interest rate is 5%, $5346.98 will be received annually from the 7th year