AlexBeWare1210

11.04.2020 • 

Mathematics

A thirty-year annuity X has annual payments of $1000 at the beginning of each year for twelve years, then annual payments of $2000 at the beginning of each year for 18 years. A perpetuity Y has payment of $Q at the end of each year for 20 years, then payments of $3Q at the end of each year thereafter. The PV of X, Y are equal when calculated using annual effective discount rate of 7.42%.

Find Q.

Round your answer to the nearest cent. Answer in units of dollars.

Your answer must be within ± 0.0%

Ответ:

keke6361

08.10.2021

Mathematics

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1 inch

Step-by-step explanation:

If we call the thickness of the frame x, then the dimensions of the glass are:

w = 8 − 2x

h = 10 − 2x

The area of the glass is width times height:

48 = (8 − 2x) (10 − 2x)

Distribute and simplify:

48 = 80 − 16x − 20x + 4x²

0 = 4x² − 36x + 32

0 = x² − 9x + 8

Factor and solve:

0 = (x − 1) (x − 8)

x = 1 or x = 8

x can't be more than 4 (half the width of the frame), so x = 1 inch.

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