An investment offers $5700 per year for 10 years. with the first payment occurri

Question

An investment offers $5700 per year for 10 years. with the first payment occurring one year from now. If the required return is 5 percent what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.1 6.) Present value $ What would the value be if the payments occurred for 35 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ What would the value be if the payments occurred for 65 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ 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.) Present value $

Explanation / Answer

Future value of annuity           = Periodic amount×[(1+r)^n-1]÷r

For 10 years:

= $5,700×[(1+5%)^10-1]÷5%

= $71,693.98

For 35 years:

= $5,700×[(1+5%)^35-1]÷5%

= $514,826.75

For 65 years:

= $5,700×[(1+5%)^65-1]÷5%

= $2,603,748.66

present value is unlimited if the payments will occur forver.

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