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?

Answer:

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%