Question

Suppose you just bought a 15-year annuity of $7,700 per year at the current interest rate of 11 percent per year. What is the value of your annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present value $ ?

What happens to the value of your investment if interest rates suddenly drop to 6 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $?

What if interest rates suddenly rise to 16 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present Value $ ?

Answer 1

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 7700[1- (1+ 0.11)^-15]/ 0.11

= 7700[1- (1.11)^-15]/ 0.11

= 7700[1- 0.209004346650319]/ 0.11

= 7700[0.790995653349681/ 0.11]

= 7700[7.19086957590619]

= 55369.7

So PV of the annuity is $55369.7

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If the interest rate drop to 6% then PV of annuity will be

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 7700[1- (1+ 0.06)^-15]/ 0.06

= 7700[1- (1.06)^-15]/ 0.06

= 7700[1- 0.41726506073554]/ 0.06

= 7700[0.58273493926446/ 0.06]

= 7700[9.71224898774099]

= 74784.32

So PV of the annuity is $74784.32

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If the interest rate rise to 16% then PV of annuity will be

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 7700[1- (1+ 0.16)^-15]/ 0.16

= 7700[1- (1.16)^-15]/ 0.16

= 7700[1- 0.107927013982015]/ 0.16

= 7700[0.892072986017985/ 0.16]

= 7700[5.5754561626124]

= 42931.01

So PV of the annuity is $42931.01

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Hope that helps.

Feel free to comment if you need further assistance J