PSAT Math - How to find simple interest

Peter wanted to buy a car and borrowed $2,500 from the bank at 5% simple interest per year. He was able to pay back the loan in one lump sum at six months. What was the total amount he paid the bank?

$$2562.50$

$$3250.75$

$$3000$

$$2750.25$

$$2625.50$

Explanation

Simple interest is given by $i=prt$ where $i$ = interest, $p$ = principal, $r$ = rate, and $t$ = time in years.

$i=2500\cdot (0.05)(0.5)=$62.50$

Remember, six months is the same as half of a year. The total paid back to the bank is the principle plus the interest, or $2,562.50.

You really want to buy a car that costs $15,000 but you only have $5,000 saved. Rather than getting a bank loan, your parents offer to lend you the extra money but will require you to pay them back with 4.3% interest. How much will car cost in total after you have paid your parents back?

Explanation

Amount borrowed = $15,000 – $5,000 = $10,000

Interest of 4.3% = $10,000 * 0.043 = $430

Total cost of car = $5000 + $10000 + $430 = $15,430

Ted works over the summer and makes $9 per hour. He works for 20 hours each week for 10 weeks. After paying 10% in taxes, he buys a bike for $500 and puts the rest of his money in the bank.

If Ted's bank pays 5% interest on the total sum once per year, and Ted doesn't add or remove anything from the account, how much money (rounded to the nearest cent) will Ted have in 5 years?

Explanation

To start, we see that Ted works for 20 hours per week for 10 weeks. This means he works a total of 200 hours over the summer. He is paid $9 dollars each hour. Therefore he makes $9 x 200 hours = $1800 total over the summer. He then has to pay 10% in taxes, or .1 x $1800, leaving him with . He buys the bike for $500, so he has $1620 - $500 = $1,120 to deposit at the bank.

Now we have to find out how much he will have 5 years later. Since the bank pays 5% interest each year, we know that he will make 5% of what he has each year. He starts with $1,120. 5% of this value is $$1120\cdot .05=$56$ . Adding this to the original $1,120 gives us $1,176.

This is also the same as multiplying instead by 1.05. We repeat this step 5 times, giving us:

$$1,120*(1.05)^{5} = $1,120 * 1.276... = $1,429.435... = $1,429.44$

Jane borrows dollars from the bank. Her loan has an annual interest rate of percent. How much interest will she owe after years? (Use a simple interest calculation)

Explanation

Use the simple interest formula:

Interest equals the initial amount multiplied by the annual interest rate multiplied by the number of years:

$I = P\cdot {r}\cdot {t}$

Let = interest owed

Let = principal (aka the initial amount of the loan)

Let = interest rate

Let = years passed

Therefore:

I have $100 in my bank. After one year, I have withdrawn a total of $20 and I still have $85 in the bank. What is the yearly interest rate of my bank account?