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ACT Math : Arithmetic

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Example Questions

Example Question #1 : How To Find Simple Interest

An account accrues simple interest on an initial balance of $\$350$ dollars at a rate of $4.5\%$ per year. After years, how much interest has accrued to the account?

Possible Answers:

$\$160.75$

$\$147.84$

$\$157.50$

$\$193.54$

$\$167.42$

Correct answer:

$\$157.50$

Explanation:

Simple interest has the formula of:

I=P*R*T , where is the starting balance, is the interest rate, and is the number of accrual periods.

For our data, this is simply:

I=350*0.045*10=157.5

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Example Question #6 : How To Find Simple Interest

The equation I = prt 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 man pays $\$ 33600$ in annual interest on a loan of $\$ 42000$ . If the loan repayment term was years, what was the interest rate?

Possible Answers:

$5 \%$

$10 \%$

$13 \%$

$6 \%$

$8 \%$

Correct answer:

$8 \%$

Explanation:

Plugging our variables into the above equation gives us

33600 = (42000)(r)(10)

$r = \frac{33600}{(42000)(10)} = .08$

Thus, our interest rate is $8 \%$ .

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Example Question #7 : How To Find Simple Interest

Grant takes out a personal loan to buy a car. He pays $\$ 3125$ in interest before the loan is repaid. If the interest rate is $5 \%$ compounded annually and it took Grant years to repay the loan, what amount was the original loan for?

Possible Answers:

$\$ 17500$

$\$ 15000$

$\$ 10000$

$\$ 12500$

$\$ 7500$

Correct answer:

$\$ 12500$

Explanation:

Using the I = prt equation gives us:

$\$ 3125 = (p)(.05)(5)$

$p = \frac{3125}{(.05)(5)} = \$ 12500$

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Example Question #8 : How To Find Simple Interest

Ashley wants to take out a loan for some home improvements. She knows that her simple interest rate will be $1.55 \%$ monthly, and that she will need to borrow $\$ 5000$ . If she wants to pay no more than $\$ 2325$ 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:

Explanation:

Using the I = prt equation gives us:

2325 = (5000)(.0155)(t)

$t = \frac{2325}{(.0155)(5000)} = 30$

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Example Question #1 : How To Find Simple Interest

A loan officer realizes an error has been committed on an account -- a customer with a $\$ 70000$ loan has been paying an annual interest rate of $3.55 \%$ for the last years instead of the promised annual interest rate of $2.55 \%$ . If the loan was just paid off, how much money does the bank owe the customer?

Possible Answers:

$\$ 13000$

$\$ 9000$

$\$ 5000$

$\$ 7000$

$\$ 11000$

Correct answer:

$\$ 7000$

Explanation:

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

I = prt = (70000)(0.0355)(10) = 24850

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

I = prt = (70000)(0.0255)(10) = 17850

Lastly, find the difference between these two numbers:

$24850-17850 = \$ 7000$

Thus, the bank owes the customer $\$ 7000$ .

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Example Question #10 : How To Find Simple Interest

How much more money will a savings account at $3 \%$ annual simple interest generate than an account at $2 \%$ , if both accounts start with $\$ 500$ and are left untouched for years?

Possible Answers:

$\$ 125$

$\$ 90$

$\$ 120$

$\$ 155$

$\$ 170$

Correct answer:

$\$ 90$

Explanation:

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

I = prt = (500)(.03)(18) = 270

I = prt = (500)(.02)(18) = 180

I_1 - I_2 = 270-180 = 90

So, the account at $3 \%$ interest saves $\$ 90$ more.

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Example Question #1261 : Act Math

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 $2.5 \%$ , and Antoine contributed $\$ 5000$ to his savings account when the year ended, how much interest is he entitled to?

Possible Answers:

$\$ 75$

$\$ 540$

$\$ 300$

$\$ 125$

$\$ 400$

Correct answer:

$\$ 125$

Explanation:

If the profit was $2.5 \%$ and the contributions were $\$ 5000$ , then we can use the equation I = prt , where is the principal, is the rate and is the number of periods of time interest is applied (in this case, t=1 since this is a one-time payout).

$I = prt = (\$ 5000)(.025)(1) = \$ 125$

Thus, Antoine is entitled to $\$ 125$ in interest.

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Example Question #1261 : Act Math

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:

$\$ 8880$

$\$ 9900$

$\$ 12000$

$\$ 10600$

$\$ 13200$

Correct answer:

$\$ 9900$

Explanation:

The simple interest formula is,

$P\left ( 1+rY\right )$ where is the principal, is th rate of interest, and is the number of years. So,

$55\textup{,}000(1+.03\left ( 6\right ))=64\textup{,}900$

$64\textup{,}900-55\textup{,}000=9900$

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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:

$23.90

$19.50

$10.50

$20.40

Correct answer:

$20.40

Explanation:

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

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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:

$125

$100

$140

$200

Correct answer:

$140

Explanation:

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

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

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ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Simple Interest

Example Question #6 : How To Find Simple Interest

Example Question #7 : How To Find Simple Interest

Example Question #8 : How To Find Simple Interest

Example Question #1 : How To Find Simple Interest

Example Question #10 : How To Find Simple Interest

Example Question #1261 : Act Math

Example Question #1261 : Act Math

Example Question #1 : How To Find The Sale Price

Example Question #1 : How To Find The Sale Price

All ACT Math Resources

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