Determine the value of the investment at the end of 5 years. Write a function f that determines the value of the investment (in dollars) in terms of the number of years t since the investment was made. What is the annual percent change (APY) for the account?

Complete Question:

Suppose that $1500 is invested in an account with an APR of 3.1% compounded continuously.   Determine the value of the investment at the end of 5 years.   Write a function that determines the value of the investment in terms of the number of years , since the investment was made.    What is the annual percent change for the account?

Function that determines the value of the investment f(t) = 1500 exp(rt)

Investment after 5 years, f(5) = $1751.49

Annual Percent change = 3.14%

Explanation:

Function that determines the value of the investment

Initial amount invested, f₀ =  $1500

f(t) = f₀ exp(rt)

f(t) = 1500 exp(rt)

r = 3.1% = 3.1/100 = 0.031

f(t) = 1500 exp(0.031t)

Value of the investment at the end of 5 years:

f(5) = 1500 exp (0.031 *5)

f(5) = $1751.49

c) Annual Percentage Change for the account

Get the increase in investment after one year

f(1) = 1500 exp(0.031)

f(1) = $1547.23

Annual Percent yield = [(New Investment - Original investment)/ Original investment] * 100%

Annual Percent yield = [(1547.23 - 1500)/1500] * 100%

Annual Percent yield = (47.23/1500) * 100

Annual Percent yield = 3.14%

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