Algebra - How to find simple interest

If you deposit into a savings account that yields 5% annual interest, how much interest will you earn in years?

Explanation

When finding simple interest, we use the following formula:

$\text{Simple Interest (I)} = \text{Principal (P)} \cdot \text{Rate (R)} \cdot \text{Time (T)}$

The principal (P) equals the amount we deposit or invest. In this case,

The rate (R) is the percentage rate at which the principal increases or decreases. In this case,

because we must convert 5% into decimal form.

The time (T) equals the number of years the money is accruing interest. In the case,

So, according to the formula above

$I = P \cdot R \cdot T$

$I = 2500 \cdot 0.05 \cdot 3$

Therefore, the total interest earned is $375.

Oscar spent on his credit card for a Valentine's Day on the town with his better half. If the monthly billing statement totalled , what is the monthly interest on Oscar's card?

Explanation

To find the percent interest, we want to determine the cash value,of the interest and divide that by the card balance before interest was accrued:

$\frac {$242.36-$217.65}{$217.65}=\frac {$24.71}{$217.65}=0.114$

$0.114\cdot100%=11.4%$

Sal invests $2000 in a fund and after a year, earns $140 of interest. What is the interest rate for the fund Sal invested in?

Explanation

To calculate the percent interest of Sal's account, we arrange the simple interest formula:

Solve for the interest rate,

$r=\frac{I}{pt}$

Plug in the appropriate values

$r=\frac{140}{(2000)(1)}$

Simplify.

If a woman invests $2000 into a fund that has 5% annual interest, how much many can she expect to make from her investment, after 2 years?

Explanation

To calculate the amount of interest she earned, we use the formula:

, where is the principal (the initial amount invested) is the interest rate, and is the amount of time, in years, passed.

Plug the given values into the above formula:

Remember, when calculating interest, percents needed to be converted to decimals.

Exactly one year ago, John placed $8,000 into an investment account. Over the past year, the investments in his account have increased in value by 12%. How much money does he have now?

Explanation

John started out with $8,000 and increased it by 12% after a year. This indicates that by the end of the year, he has 112% of $8,000 (The original $8,000 plus the 12% return from his investments). Convert 112% into its decimal equivalent of 1.12 and multiply it by $8,000 to get John's current savings amount:

Cody has fallen behind on his student loan payments and has not made a payment in a year. The original balance of has accrued interest and increased to . If Cody does not make any payments this year, what will be the year-end balance of the loan?

Explanation

To calculate next year's balance with added interest, we want to know the interest rate. We can determine this by dividing the interest already accrued by the initial loan balance:

$\frac{$13,116.00-$12,000.00}{$12,000}=\frac{$1,116}{$12,000}=0.093$

$0.093\cdot100%=9.3%$

Now that we know the annual interest rate, we can calculate the balance after one year with interest:

$$13,116.00\cdot\frac{9.3%}{100%}=$1,219.79$

Once we've calculated the interest, we can add it to our starting balance to calculate the new balance with added interest:

You invest $550 in a savings account that accrues interest at a rate of 6% annually. How much interest will you earn after 3 years?

Explanation

To find simple interest, we use the following formula:

$\text{simple interest} = P \cdot R \cdot T$

where

$P = \text{principal or amount deposited}$

$R = \text{percentage rate}$

$T = \text{time in years}$

Given what we know

$R = 6% \text{ or } 0.06$

$T = 3 \text{ years}$

we can substitute into the formula. We get

$\text{simple interest} = $550 \cdot 0.06 \cdot 3$

$\text{simple interest} = $99$

Therefore, you earned a total of in simple interest.

Oscar takes out a loan from the bank for . If the end of the month billing statement has a total balance of , what is the monthly interest rate for the loan?

Explanation

The monthly interest rate is the percent of the principal value of the loan added on to the total balance each month. We can determine the interest rate by dividing the interest accrued by the initial loan amount:

$\frac{$2,136-$2,000}{$2,000}=\frac{136}{2,000}=0.068\ 0.068\cdot100%=6.8%$

Find the simple interest earned if you deposit $2000 into a bank at an annual rate of 5% for 3 years.

Explanation

To find the simple interest, we use the formula

$\text{simple interest} = \text{principal} \cdot \text{rate} \cdot \text{time}$

$SI = P \cdot R \cdot T$

where the principal is the initial amount we desposit, the rate is the percentage of interest accruing, and the time is the number of years.

We know

$R = 5% \ \text{or} \ 0.05$

So we substitute, and we get

$SI = $2000 \cdot 0.05 \cdot 3$

Therefore, the simple interested earned is $300.

Carly invested in a savings account, which, within a years' time increased by roughly . If at the end of the year, Carly withdrew of the total balance in the savings account, what is the remaining balance?