Question

1. Future value

The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value.

The process for converting present values into future values is called _______ . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?

• The inflation rate indicating the change in average prices

• The interest rate (I) that could be earned by invested funds

• The present value (PV) of the amount invested

• The duration of the investment (N)

All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or Investment period. Each line on the following graph corresponds to an interest rate: 0 %, 8 %, or 16 %. Identify the interest rate that corresponds with each line.

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 of principal, the Interest rate, and the investment or deposit period-to the amount deposited or Invested In order to compute the amount of Interest. However, the two methods differ in their relationship between the variables.

Assume that the variables I, 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:

Identify whether the following statements about the simple and compound interest methods are true or false.

Statement

After the end of the second year and all other factors remaining equal, a future value based on compound interest will exceed a future value based on simple interest.

All other factors being equal, both the simple interest and the compound interest methods will not generate the amount of earned interest by the end of the first year.

Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest.

Mia is willing to invest $35,000 for six 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 six-year Investment period, complete the following table and indicate whether Mia should invest in each of the investments.

Note: When calculating each investment's future value, assume that all interest is earned annually. The final value should be rounded to the nearest whole dollar.

Answer 1

1). The process for converting present values into future values is called compounding.

2). The variable not required for compounding is inflation rate. (option a)

3). Line A - interest rate 16%

Line B - interest rate 8%

Line C - interest rate 0%

Basically, with higher interest rate, the future value due to compounding will be higher.

4). Investments and loans base their interest calculations on simple interest and compound interest methods.

5). Compound interest formula: FV = PV*(1+I)^N

Simple interest formula: FV = PV + (PV*I*N)

6). Statement 1 is true. By the end of 2nd year, a future value based on compound interest will be greater than one based on simple interest.

Statement 2 is false. By the end of 1st year, future values based on compound interest and simple interest will be identical as compounding period is one.

Statement 3 is true. An account earning compound interest will grow much faster than a similar account earning simple interest.

7). Investment L: Expected future value = PV*(1+I)^N = 35,000*(1+7%)^6 =52,526

Investment M: Expected future value = PV + (PV*I*N) = 35,000*(1 + 6%*6) = 47,600

Investment P: Expected future value = PV*(1+I)^N = 35,000*(1+11%)^6 = 65,465

She can make any of the three investments but comparatively, investment P is the best investment as it gives the highest future value.