Business Math Paper

Annuities

Businesses, financial institution, and other organizations invest in annuities to raise money to pay such expenses as bond debts, notes due, or stock dividends. They also invest in annuities to provide for future needs, such as new facilities and equipment or employee retirement benefits. Individuals may purchase annuities, such as an Individual Retirement Account (IRA), or an insurance policy, from insurance companies, financial institutions, or securities brokers.

An ordinary annuity is a series of regular payments where each payment is made at the end of the payment period. The payment period is the length of time between payments. Payments are usually made annually, semiannually, quarterly, or monthly. The term of the annuity is the length of time from the beginning of the first payment period to the end of the last payment period. The amount of the annuity is the sum of all payments plus their accumulated interest. Their amount is also called the cash value.

The amount of an annuity can be found by using the Amount of an Annuity table. The table lists the value of an annuity of $1 compounded at various rates for various time periods. To find the amount of an ordinary annuity using the annuity table, multiply the payment by the appropriate table value. The interest earned can be found by subtracting the sum of the payments from the amount of the annuity.

For example:

Brian purchased an ordinary annuity from an investment broker at 8% interest compounded semiannually. If he semiannual deposit is $150, what is the amount of the annuity and the interest earned at the end of 10 years?

Step 1. Find the number of compounding periods and the rate per period.

Periods Compounding years x per year = Periods

10 x 2 = 20

Annual Periods Rate per rate / per year = Period

8% / 2 = 4%

Step 2. Locate the table value on the Amount of an Annuity table. The table value for 20 periods at 4% is 29.77808.

Step 3. Find the amount of the annuity.

Payment x Table Value = Amount of Annuity

$150 x 29.77808 = $4,466.71

Step 4. Find the interest earned.

No. of Total payment x payments = Payments

$150 x 20 = $3,000

Step 5.

Amount of Annuity - Total Payment = Interest

$4,466.77 - $3.000 = $1,466.71

Interest Rates and Loans

Most People have money in a savings account and wonder how to figure out the actual interest rates or the APR (annual percentage yield). To find the amount of interest you would use this formula: P (principle) x R (rate) x T (time) = I (interest)

Example:

$1000 x 3% x 1 year. = $30

Interest is the fee paid for borrowing money. Most individuals or business owners pay simple interest on a short-term loan, which is usually a loan of up to 1 year. The amount of interest charged by a bank depends on three factors:

1. The amount borrowed is called the principal.

2. The length of time the money is borrowed.

3. The rate of interest charged.

The interest rate assigned to a loan may vary widely according to such factors as the prime rate set by the bank, the credit rating of the borrower, and general economic conditions. The prime rate is the interest rate assigned to the institution's best customers. Simple interest is calculated on the amount borrowed. Principal x rate x time = interest or P X R x T = I

When a loan is due, the borrower must pay back the maturity value, which is the principal plus interest.

For example:

To find the simple interest charged on a loan of $450 at 12% for 1 year. Find the maturity value due after 1 year.

Solution:

Step 1. Find the simple interest.

Principal x Rate x Time = Interest

$450 x 12% x 1 = $54

How to calculate the maturity value

(MV) maturity value = Principal + Interest