Growth Facotr

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Suppose you are given two different options to invest in at your bank. Option A allows you to deposit $1,500 at 7.5% compounded quarterly, or Option B allows an investment of $2200 compounded continuously at 6.5%.

a. Write a function g that models the amount of money earned using option A as an investment for t number of years. What is the quarterly growth factor? What is the annual growth factor? What is the effective yield?

b. Write a function h that models the amount of money earned using option B as an investment for t number of years. What is the annual growth factor? What is the effective yield?

c. During what time period will option A be less than or equal to Option B. Round your year value to the nearest hundredth. Show work and/or explain how you got your answer.

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@PaulaPolly,

a) The number of quarterly payments is t*4. The quarterly interesting rate is 7.5%/4. The amount of money after T years is g = $2,200*(1+7.5%/4)^(t*4). The effective yield is the yield after one year, so just compute (1+7.5%/4)^4

b) The function for continuous interest is h = exp(I * t) where I=interest rate or 6.5% and t is the time in years. Once again, for the annual growth factor, put in t=1 year.

c) Graph these two against each other and find when (b) is greater than (a). Remember that (a) has steps to it. You only get interest every quarter. (b) is a smooth line.

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Growth Facotr

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