Question

Cameron is going to receive an annuity for 44 years of $27,833, and Kennedy is going to receive a perpetuity of that same amount. If the appropriate discount rate is 6%, how much more are Kennedy's cash flows worth today than Cameron's cash flows? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Answer 1

Answer: $36,173.622

Explanation:

Cameron:

Annual Payment  = $27,833

Time Period(n) = 44 years

Discount Rate(r) = 6%

$Present\ Worth=Annual\ Payment\times[\frac{(1-(\frac{1}{1+r})^{n} }{r}]$

$Present\ Worth=27,833\times[\frac{(1-(\frac{1}{1.06})^{44} }{0.06}]$

$= 27,833\times\frac{1-0.078}{0.06}$

$=27,833\times15.367$

= $427,709.711

Kennedy:

Annual Payment = $27,833

Discount Rate = 6%

Present Worth = $\frac{27,833}{0.06}$

Present Worth = $463,883.333

So, Present Worth of Kennedy is $36,173.622 more than that of Cameron.