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Mo will receive a perpetuity of $32,000 per year forever, while Curly will receive the same annual payment for the next 40 years. If the interest rate is 7.6 percent, how much more are Mo's payments worth?

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Kolawole845

Answer:

Mo payment is worth more than Curly by $22,482.55

Explanation:

To determine the the amount by which Mo's payment is worth more than the Curly, find the difference between their present value of their payments.

Mo

The present value (PV) of a perpetuity is determined as follows;

PV of perpetuity = A/r

A- annual payment - 32,000,r- 7.6%

PV = 32,000/0.076 =   421,052.63

Curly

PV of an annuity is given as follows:

PV =A×  ( 1-(1+r)^(-n))/r

n- number of years -40, r-7.6%, A-annual payment- 32,000

PV = 32,000× (1- (1.076)^(-40))/0.076

PV =  $398,570.08

Mo payment is worth more than Curly by the

Difference =   $421,052.63 -  $398,570.08 =  22,482.55

Mo payment is worth more than Curly by 22,482.55

Mo payment is worth more than Curly by $22,482.55

  • The calculation is as follows:

The present value (PV) of a perpetuity is determined as follows;

PV of perpetuity = A ÷ r

A- annual payment - 32,000,r- 7.6%

PV = 32,000 ÷ 0.076 =   421,052.63

Curly

PV of an annuity is given as follows:

PV =A×  ( 1-(1+r)^(-n)) ÷r

PV = 32,000× (1- (1.076)^(-40)) ÷ 0.076

PV =  $398,570.08

Now

Mo payment is worth more than Curly by the

Difference =   $421,052.63 -  $398,570.08

=  22,482.55

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