# Simple Interest - Financial Management

Simple interest is the interest paid (in the case of borrowed money) or earned (in the case of invested money) on the principal only. The amount of simple interest is equal to the product of the principal times the rate per time period times the number of time periods:

I = PV0*i *n

where I = the simple interest in dollars; PV0 = the principal amount at time 0, or the present value; i = the interest rate per time period; and n = the number of time periods. The following problems illustrate the use of Equation .

1. What is the simple interest on $100 at 10 percent per annum for six months? Substituting$100 for PV0, 10 percent (0.10) for i, and 6⁄12 (0.5) for n yields the following:
I = $100*0.10* 0.5 =$5
2. If Isaiah Williams bought a house and borrowed $30,000 at a 10 percent annual interest rate, what would be his first month’s interest payment? Substituting$30,000 for PV0, 10 percent (0.10) for i, and 1⁄12 for n yields the following:
I = $30,000*0.10*1/12 =$250
3. Mary Schiller receives $30 every three months from a bank account that pays a 6 percent annual interest rate. How much is invested in the account? Because PV0 is the unknown in this example, Equation is rearranged: PV = PMT [I-(I+i)*n] / i Substituting$30 for I, 0.06 for i, and 1/4 (0.25) for n yields the following:

PV0 = $30 / 0.060.25 =$2,000

It also is useful to be able to calculate the amount of funds a person can expect to receive at some point in the future. In financial mathematics, the terminal, or future, value of an investment is called FVn and denotes the principal plus interest accumulated at the end of n years. It is written as follows:

FVn= PV0 + I
4. Raymond Gomez borrows $1,000 for 9 months at a rate of 8 percent per annum. How much will he have to repay at the end of the 9-month period? Combining Equations to solve for FVn results in the following new equation: FVn= PV0 + (PV0*i *n) Substituting$1,000 for PV0, 0.08 for i, and 3⁄4 (9 months = 3⁄4 of 1 year) for n yields the following:

FV3⁄4 = $1,000 + (1,000 *0.08 *3⁄4) =$1,060

This problem can be illustrated using the following timeline:

5. Marie Como agrees to invest $1,000 in a venture that promises to pay 10 percent simple interest each year for two years. How much money will she have at the end of the second year? Using Equation and assuming two 10 percent simple interest payments, the future value of Marie’s investment at the end of two years is computed as follows: FV2 = PV0 + (PV0*i *2) =$1,000 + ($1,000*0.10 *2) =$1,200

This problem can be illustrated using the following timeline:

In general, in the case of simple interest, the future, or terminal, value (FVn) at the end of n years is given by Equation.