Question

Investments and loans base their interest calculations on one of two possible methods: the interest and the interest methods. Both methods apply three variables-the amount the interest rate, and the investment or deposit period-to the amount deposited or invested in order amount of interest. However, the two methods differ in their relationship between the variables. Assume that the variables r, n, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? FV = PV + (PV Times r Times n) FV = PV Times (1 + r)^n FV = (1 + r)^n/PV Simple interest? FV = PV + (PV Times r Times n) FV = PV/(1 Times r Times n) FV = PV - (PV Times r Times n) Identify whether the following statements about the simple and compound interest methods are true or false. The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods. After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest. All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year. Laura is willing to invest $45, 000 for eight years, and is an economically rational investor. She has identified three investment alternatives (L, M, and P) that vary in their method of calculating interest and in the annual interest rate offered. Since she can only make one investment during the eight-year investment period, complete the following table and indicate whether Laura should invest in each of the investments.

Answer 1

1. FV = PV Times (1 + r)^n
2. FV = PV + (PV Times r Times n)
3. False
4. False
5. True
6. Laura should invest in investment P

Investment = L  FV = $66,485.49  Make this investment? No

Investment = M  FV = $59,400  Make this investment? No

Investment = P  FV = $77,318.37  Make this investment? Yes

Explanation:

1. Compound interest: FV = PV Times (1 + r)^n
2. Simple interest: FV = PV + (PV Times r Times n)
3. The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods. False
4. After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest. False
5. All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year. True

Investment = L

Interest rate and method = 5% compound interest

Expected Future Value, FV = PV (1 + r)^n

FV = 45000 (1 + 0.05)^8

FV = 45000 * (1.05)^8

FV = 45000 * 1.477455 = $66,485.49

Make this investment? Yes / No

Investment = M

Interest rate and method = 4% simple interest

Expected Future Value, FV = PV + (PV * r * n)

FV = 45000 + (45000 * 0.04 * 8)

FV = 45000 + 14400 = $59,400

Make this investment? Yes / No

Investment = P

Interest rate and method = 7% compound interest

Expected Future Value, FV = PV (1 + r)^n

FV = 45000 (1 + 0.07)^8

FV = 45000 * (1.07)^8

FV = 45000 * 1.718186 = $77,318.37

Make this investment? Yes / No

Since she can only make one investment during the eight-year investment period, Laura should invest in investment P