four years ago, lucas invested $500. three years ago, matt invested $600. today, these two investments are each worth $800. assume each account continues to earn its respective rate of return and interest is compounded annually. which one of the following statements is correct concerning these investments?

When an investment earns interest that is compounded annually, it means that both the amount invested and the interest that has already been earned increases at an exponential rate once a year.

The formula that would use to determine the interest rate earned on the investment is:

Interest rate =[(FV / PV)^(1 / n)] - 1

Where:

FV = future value
PV = present value
n = number of years

Lucas's interest rate = [ (800 / 500)^(1/3) ]- 1 = 16.96%

Matt's interest rate = [ (800 / 600)^(1/3) ]- 1 = 10.06%

Value of Matt's investment three years from today = 800 x (1.1006)^3 = $1,066.67

Value of Lucas investment three years from today = 800 x (1.1696)^3 = 1,2799.77

Value of Matt's investment one year ago = 600 x (1.1006)^2 = 726.79

Value of Lucas investment one year ago = 500 x (1.1696)^2 = 683.98

Here are the options:

A) Three years from today, Matt's investment will be worth more than Lucas

B) One year ago, Lucas investment was worth less than Matt's investment.

C) Matt earns a higher rate of return than Lucas

D) Matt has earned an average annual interest rate of 9.86 percent.

E) Lucas has earned an average annual interest rate of 12.64 percent.

To learn more about compound interest, please check: https://brainly.com/question/26367706

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