Bad Company, Inc., has a major outlay of $1.7 million that is needed to renovate the company's manufacturing facility. Because the company's management is conservative, it won't undertake the renovation until it has the cash necessary to fund the renovation. The company plans to deposit $134,000 each quarter into an account that will earn 1.35 percent per quarter. How many years will it be until the company has the money saved for the renovation?

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TomShelby TomShelby · Answer 1 · 2019-10-24T07:45:33+02:00

Answer:

It will require deposists for 11.79 years

Explanation:

We need to solve for the time at which an ordinary annuity of 134,000 each quarter at 1.35% rate generates a future value of 1,700,000

[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex]

C $134,000.00

time n

rate 0.0135

FV $17,000,000

[tex]134000 \times \frac{(1+0.0135)^{n} -1}{0.0135} = 1,700,000\\[/tex]

we rearrenge and solve as we can:

[tex](1+0.0135)^{n}= 1 + \frac{1700000\times0.0135}{134000}[/tex]

[tex](1+0.0135)^{n}= 1.17126866[/tex]

Then use logarithmics properties to solve the equation:

[tex]n= \frac{log 1.17126866}{log(1+0.0135)[/tex]

n = 11.78905103