### All ACT Math Resources

## Example Questions

### Example Question #4 : How To Find Simple Interest

The equation can be used to calculate simple interest, where is the total interest, is the principal amount, is the rate of interest expressed as a decimal and is the amount of times interest is added.

Grant takes out a personal loan to buy a car. He pays in interest before the loan is repaid. If the interest rate is compounded annually and it took Grant years to repay the loan, what amount was the original loan for?

**Possible Answers:**

**Correct answer:**

Using the equation gives us:

### Example Question #5 : How To Find Simple Interest

The equation can be used to calculate simple interest, where is the total interest, is the principal amount, is the rate of interest expressed as a decimal and is the amount of times interest is added.

Ashley wants to take out a loan for some home improvements. She knows that her simple interest rate will be monthly, and that she will need to borrow . If she wants to pay no more than in interest over the life of the loan, what is the longest amount of time in months she has to pay off the loan?

**Possible Answers:**

**Correct answer:**

Using the equation gives us:

### Example Question #6 : How To Find Simple Interest

The equation can be used to calculate simple interest, where is the total interest, is the principal amount, is the rate of interest expressed as a decimal and is the amount of times interest is added.

A loan officer realizes an error has been committed on an account -- a customer with a loan has been paying an annual interest rate of for the last years instead of the promised annual interest rate of . If the loan was just paid off, how much money does the bank owe the customer?

**Possible Answers:**

**Correct answer:**

First, we must use our formula to determine how much money the customer has paid in interest:

Now, calculate how much *should *have been paid, based on the correct interest rate:

Lastly, find the difference between these two numbers:

Thus, the bank owes the customer .

### Example Question #1261 : Act Math

How much more money will a savings account at annual simple interest generate than an account at , if both accounts start with and are left untouched for years?

**Possible Answers:**

**Correct answer:**

First, we must use our formula to determine how much interest each account generates, then subtract the greater from the smaller.

So, the account at interest saves more.

### Example Question #11 : Interest

A credit union pays out interest to its members proportional to their contributions to savings accounts at the end of each financial year in which the union posts a profit. If at the end of the year, the credit union posts a profit of , and Antoine contributed to his savings account when the year ended, how much interest is he entitled to?

**Possible Answers:**

**Correct answer:**

If the profit was and the contributions were , then we can use the equation , where is the principal, is the rate and is the number of periods of time interest is applied (in this case, since this is a one-time payout).

Thus, Antoine is entitled to in interest.

### Example Question #11 : How To Find Simple Interest

What interest is expected to be paid on a loan for $55,000 with 3% interest compounded annually over a period of 6 years?

**Possible Answers:**

**Correct answer:**

The simple interest formula is,

where is the principal, is th rate of interest, and is the number of years. So,

### Example Question #1 : How To Find The Sale Price

Max wants to buy a couch at The Furniture Store. The couch he is considering had been marked on sale for 20% off and was selling for $320. The day he comes in to buy the couch, it has been marked down an additional 40% off of the sale price. What is the difference in the original price of the couch and what Max paid for the couch?

**Possible Answers:**

$160

$128

$208

$240

$272

**Correct answer:**

$208

(320) / (0.8) = 400. The couch has been marked down an additional 40% from the sale price of $320. $320 * 0.6 = $192. $400 – $192 = $208.

### Example Question #1 : How To Find The Sale Price

Mary wants to buy a new skirt. It was originally $30, but is marked 20% off. She also received a coupon for 15% off the sale price. How much will Mary pay for the skirt?

**Possible Answers:**

$10.50

$23.90

$19.50

$20.40

**Correct answer:**

$20.40

20% off means that the new price of the skirt will be 80% of the original price:

$30(100% – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100% – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

### Example Question #1 : How To Find The Sale Price

A tablet computer listed at an original price of $250 is placed on sale for 20% off the original price. Bob, an employee of the store, gets an additional 30% off the sale price. What price would Bob pay to purchase the tablet computer?

**Possible Answers:**

$200

$140

$125

$100

**Correct answer:**

$140

Take the original price and take off 20% = $250(1 - .2) = $250(.8) = $200

Then take off another 30% $200(1 - .3) = $140

### Example Question #1 : How To Find The Sale Price

The manager of a department store decided to raise the price of a certain pair of shoes by 30%. The next day, the store ran a sale of 20% off all items. What is the difference in price, in percentage terms, between the initial price of the shoes and the sale price?

**Possible Answers:**

The price increased by 10%

The price increased by 4%

The price decreased by 10%

The price increased by 1.5%

The price decreased by 4%

**Correct answer:**

The price increased by 4%

To find the price after the initial 30% increase by the manager, you must multiply the original price by 1.3. Then, to find the price after the 20% off sale, you must multiply the new price by 0.8. The original price, therefore, is being multiplied by 1.3*0.8 = 1.04, indicating a 4% overall increase.

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