Respuesta :
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%
