Appendix G: Time Value of Money

What is the first variable (dollars to be paid) made up of?

1. A series of interest payments (an annuity) 2. The principal amount (a single sum)

What's the other method used to compute the future value of a single amount involve? What do you do?

1. It involves a compound interest table that shows future value of 1 for n periods. 2. You multiply the principal amount by the future value factor for the specified number of periods and interest rate.

Example: Assume you invest $2,000 at the end of each year for three years at 5% interest compounded annually. How would you calculate the future value of the annuity?

1. Take the $2,000 invested in year 1 and multiply it by the future value factor for 2 periods since 2 years of interest will accumulate on it. 2. Second $2,000 investment will only accumulate one year's/period's interest (in year 3) and is only multiplied by the future value factor for one year. 3. The final $2,000 investment is made at the end of the third year and will not earn any interest.

What is it necessary to know in computing the present value of an annuity?

1. The discount rate 2. The number of payments (receipts) 3. The amount of the periodic receipts/payments

What is the present value based on?

1. The dollar amount to be received in the future 2. The number of periods 3. The interest rate (discount rate)

To compute the present value of a bond, what must be discounted?

1. The interest payments 2. Principal amount

In computing the future value of an annuity, what is it necessary to know?

1. The interest rate 2. The number of payments (receipts) 3. The amount of periodic payments (receipts)

What are the three variables the present value (or market price) of a long-term note or bond is the function of?

1. The payment amounts 2. The length of time until the amounts are paid 3. The discount rate

Annuity

A series of payments or receipts of equal dollar amounts.

What is simple interest?

Computed on the principle amount only. It is the return on the principal for one period.

What is the formula for future value?

FV = p x (1 + i)^n FV = Future Value p = principal (present value; the value today) i = interest rate for one period n = number of periods

What is the formula for simple interest?

Interest = Principal (p) x Rate (i) x Time (n)

When the time frame is less than one year, what is necessary? Give an example.

It is necessary to convert the annual interest rate to the applicable time. If an investor received $500 semiannually for 3 years instead of $1,000 annually, the number of periods doubles to become six and the discount rate is halved from what it was originally (i.e., 10% to 5% per period).

What is compound interest? How is it computed?

It is the return on (or growth of) the principal for two or more time periods (it computes interest not only on the principal but also on the interest on the principal). It is computed on the principal and on any interest earned that has not been paid or withdrawn.

What is the "future value of a single amount"?

It is the value at a future date of a given amount invested, assuming compound interest.

What are some examples of annuities?

Loan agreements, installment sales, mortgage notes, lease (rental) contracts, and pension obligations

Example of finding the present value of a single amount: Assume you want to invest a sum of money today that will provide $1,000 at the end of one year or a 10% rate of return. What amount would you need to invest today to have $1,000 one year from now and

PV = $1,000 (future value) / (1 + .10)^1 = $909.09 Present Value

What are the three elements that affect the amount of interest involved in any financing transaction?

Principal: The original amount borrowed or invested Interest Rate (i): An annual percentage of the principal Time (n): The number of periods that the principal is borrowed or invested.

Compound interest uses... (pg. 2)

The accumulated balance (principal plus interest to date) at each year-end to compute interest in the succeeding year, which is why the compound interest is getting larger.

What is interest?

The difference between the amount borrowed or invested (called the principal) and the amount repaid or collected.

Discounting the future amount

The process of determining the present value

Future value of an annuity

The sum of all the payments (receipts) plus the accumulated compound interest on an annuity.

What is present value?

The value now of a given amount to be paid or received in the future, assuming compound interest.

Present value of an annuity

The value now of a series of future receipts or payments, discounted assuming compound interest.