An investment offers $5,500 per year for 20 years, with the first payment occurr

Question

An investment offers $5,500 per year for 20 years, with the first payment occurring one year from now. 1.If the required return is 7 percent, what is the value of the investment?(Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) 2.What would the value be if the payments occurred for 45 years?(Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) 3.What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) 4.What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

We can use the present value of annuity in this sum:

THe formula is:

PV= A*(1-((1+r)^-n)))/r

A= annuity

r=rate of interest

n= years

1)

r= 7%, n=20

PV=$58267.08

2)

r= 7%, n=45

PV=$74830.37

3)

r= 7%, n=70

PV=$77882.14

4)

For infinite payments, n= infinity. thus the fomula becomes:

PV= A*(1)/r =5500/0.07

=$78571.43

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