### Simple Interest

*Interest* is an amount paid for the use of money. *Interest rate* is the percent paid per year. *Principal* is the amount of money on which interest is paid. *Simple interest* is interest that is computed based only on the principal, the interest rate, and the time. To calculate simple interest, use this formula:

- Interest = principal × rate × time

*I*=

*prt*

*Examples*

Martina has $300 in a savings account that pays simple interest at a rate of 3% per year. How much interest will she earn on that $300 if she keeps it in the account for 5 years?

**Procedure**

*What must you find?*Amount of simple interest*What are the units?*Dollars*What do you know?*Rate = 3% per year, time = 5 years, principal = $300*Create an equation and solve.*

*I*= ($300)(0.03)(5)

*I*= $45

Five years ago, Robin deposited $500 in a savings account that pays simple interest. She made no further deposits, and today the account is worth $750. What is the rate of interest?

*Procedure*

*What must you find?*Rate of simple interest*What are the units?*Percent per year*What do you know?*Interest = $250 ($750 – $500); principal = $500; time = 5 years

*Create an equation and solve.*

### Compound Interest

*Compound interest* is the interest paid on the principal and also on any interest that has already been paid. To calculate compound interest, you can use the formula *I* = *prt*, but you must calculate the interest for each time period and then combine them for a total.

*Example*

Ricardo bought a $1,000 savings bond that earns 5% interest compounded annually. How much interest will he earn in two years?

*Procedure*

*What must you find?*Amount of compound interest*What are the units?*Dollars*What do you know?*Principal = $1,000; rate = 5%; time = 2 years

*Create an equation and solve.*

To find the compound interest, calculate the amount earned in the first year. Add that amount to the principal, then calculate the interest earned in the second year. Total the amount of interest earned in the two years.

Year 1:

*I*=

*prt*

*I*= ($1,000)(0.05)(1)

*I*= $50

New principal = $1,050

Year 2:

*I*=

*prt*

*I*= ($1,050)(0.05)(1)

*I*= $52.50

So the total compound interest paid in two years is $50 + $52.50 = $102.50.

### Ratio and Proportion

On the ASVAB, you will almost certainly encounter word problems that will require you to work with ratios and proportions.

*Example 1 *

Kim reads an average of 150 pages per week. At that rate, how many weeks will it take him to read 1,800 pages?

*Procedure:*

*What must you find?*How long it will take to read 1,800 pages.*What are the units?*Weeks*What do you know?*150 pages read each week; 1,800 pages to be read

*Set up a proportion and solve.*

Substitute values into the equation.

Cross-multiply:

150*x* = 1,800

*x* = 12 weeks

**Example 2**

It takes 8 hours to fill a swimming pool that holds 3,500 gallons of water. At that rate, how many hours will it take to fill a pool that holds 8,750 gallons?

*Procedure:*

*What must you find?*How long it will take to fill the 8,750-gallon pool*What are the units?*Hours*What do you know?*Number of hours for 3,500 gallons*Set up a proportion and solve.*

Cross-multiply:

3500*x* = (8)(8,750)

*x* = 20 hours

**Example 3**

An airplane travels the 1,700 miles from Phoenix to Nashville in 2.5 hours. Flying at the same speed, the plane could travel the 2,550 miles from Phoenix to Boston in how many hours?

*Procedure*

*What must you find?*Time it would take to fly 2,550 miles*What are the units?*Hours*What do you know?*The plane traveled 1,700 miles in 2.5 hours

*Set up a proportion and solve.*

Substitute values.

Cross-multiply:

1,700*x* = (2.5)(2,550)

1,700*x* = 6,375

*x* = 3.75 hours

### Motion

Motion problems deal with how long it will take to get from point *a* to point *b* if you are traveling at a certain steady rate. To solve them, use this formula:

- Distance = rate × time

*d*=

*rt*

*Example*

If a racing boat travels at a steady rate of 80 miles per hour, how many miles could it travel in 3.5 hours?

*Procedure*

*What must you find?*Distance traveled in 3.5 hours*What are the units?*Miles*What do you know?*Rate = 80 miles per hour; time = 3.5 hours*Create an equation and solve.*

*d* = *rt*

Substitute values into the formula:

*d* = (80)(3.5)

*d* = 280 miles

### Percent

There are likely to be word problems involving percent on both the Arithmetic Reasoning and Math Knowledge tests of the ASVAB.

*Example 1 *

Lilly's bill at a restaurant is $22.00, and she wants to leave a 15% tip. How much money should her tip be?

*Procedure*

*What must you find?*Amount of tip*What are the units?*Dollars and cents*What do you know?*Total bill = $22.00; Percent of tip = 15*Create an equation and solve.*

Tip = 15% × 22.00

Substitute and solve.

*t* = (0.15)(22.00)

*t* = $3.30

**Example 2**

Frederick earns $1,500 per month at his job, but 28% of that amount is deducted for taxes. What is his monthly take-home pay?

*Procedure*

*What must you find?*Monthly take-home pay*What are the units?*Dollars and cents*What do you know?*Monthly pay before taxes = $1,500; percent deducted = 28%*Create an equation and solve.*

Take-home pay is 1,500 minus 28% × 1,500.

*T* = 1,500 – (1,500 × 0.28)

*T* = 1,500 – (420)

*T* = $1080

**Example 3**

40 is 80% of what number?

*Procedure:*

*What must you find?*Number of which 40 is 80%*What are the units?*Numbers*What do you know?*40 is 80% of some larger number

*Create an equation and solve.*