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"given an interest rate of 7.15 percent per year, what is the value at year t = 8 of a perpetual stream of $3,513 payments that begin at year t = 20"

Respuesta :

Aliwohaish12
This is a two part question.

First solve for the Present Value of a perpetual stream of $3513 payments, using a discount rate of 7.15%.

This calculation is pretty simple as the formula is:

Payment Amount / Interest rate
3,513÷0.0715=49,132.867132867

Then, since you won't start receiving the annual payments for another 12 years (T=20 vs T=8), you need to discount that figure back another 12 years.

That formula is

PV=FV / (1 + i)^n
PV=49,132.867132867÷(1+0.0715)^(12)
PV=21,451.91 round your answer to get 21452

In order to compute this value, the PMT that is displayed below must first be determined:

[tex]\text{= Payment} \div \text{interest rate}[/tex]  

[tex]= \$3,513 \div 7.15\%\\\\= \frac{\$3,513}{7.15\%}\\\\= \frac{\$3,513 \times 100 }{7.15}\\\\= \frac{\$351,300 }{7.15}\\\\= \$ 49132.86[/tex]

Now the value at year 8 would be  

[tex]= PMT \div (1 + \text{interest rate})^ \text{number of years} \\\\= \$49132.86 \div (1 + 7.15\%)^8\\\\= \$49132.86 \div (1 + \frac{7.15}{100})^8\\\\= \$49132.86 \div ( \frac{100+7.15}{100})^8\\\\= \$49132.86 \div ( \frac{107.15}{100})^8\\\\= \$49132.86 \div ( 1.0715)^8\\\\= \$49132.86 \div 1.7375\\\\= \frac{\$49132.86}{ 1.7375}\\\\=28277.90\\\\[/tex]

So, the value at date is [tex]\bold{\$28277.90 \approx \$28278}[/tex]

Learn more:

brainly.com/question/4550063

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