How to Find the Future Value of a Simple Interest Loan or Investment
Step 1: Identify the values you are given as principal, original amount invested, interest rate in decimal form, and number of time periods that will have elapsed.
Step 2: Substitute these values into the future value formula for simple interest loans and investments: A = P(1 + rt)
Step 3: Simplify to get your answer.
How to Find the Future Value of a Simple Interest Loan or Investment Vocabulary and Formula
Future value: The future value of a simple interest loan or investment is the value the loan will be after a certain amount of time has passed since the principal amount was borrowed or invested.
Simple interest: Simple interest is interest that is paid on the original amount invested, but not on any prior investment earned.
Simple interest rate: The simple interest rate is the percent of the original amount invested or borrowed paid each time period
Future value formula for simple interest: A = P(1 + rt) where A is the future amount, P is the principal amount, r is the simple interest rate in decimal form, and t is the number of time periods that will have passed until the future date corresponding to A.
Principal: The principal is amount invested or borrowed at the beginning of the investment or loan.
Time period: The elapsed time between the addition of interest.
Accrued interest: The accrued interest is the amount of interest accumulated
Now, we are ready to work through a couple of example problems, one with a loan and one with an investment.
How to Find the Future Value of a Simple Interest Loan or Investment: Loan Example
A loan is taken for an initial amount of $5,000 at a 6% annual simple interest rate. How much money will be owed in three years?
Step 1: Identify the values you are given as principal, original amount invested, interest rate in decimal form, and number of time periods that will have elapsed.
P = 5000
r = 0.06 since 0.06 is the decimal form of 6%
t = 3
Step 2: Substitute these values into the future value formula for simple interest loans and investments: A = P(1 + rt)
A = P(1 + rt)
A = 5000(1 + (0.06)(3))
Step 3: Simplify to get your answer.
A = 5000(1 + (0.06)(3)) Simplify the right side of the equation.
A = 5000(1 + 0.18)
A = 5000(1.18)
A = $5,900
The amount of money that will be owed in three years is $5,900.
How to Find the Future Value of a Simple Interest Loan or Investment : Investment Example
Step 1: Identify the values you are given as principal, original amount invested, interest rate in decimal form, and number of time periods that will have elapsed.
An initial deposit of $3,000 is placed in an investment earning 4.5% annual simple interest. How much will the investment be worth in 30 years?
P = 3000
r = 0.045 since 0.045 is the decimal form of 4.5%
t = 20
Step 2: Substitute these values into the future value formula for simple interest loans and investments: A = P(1 + rt)
A = P(1 + rt)
A = 3000(1 + (0.045)(20))
Step 3: Simplify to get your answer.
A = 3000(1 + (0.045)(20)) Simplify the right side of the equation.
A = 3000(1 + 0.9)
A = 3000(1.9)
A = $5,700
The investment will be worth $5,700 in 20 years.
