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**SIMPLE INTEREST**

Simple interest is the additional amount of money to the principal, sometimes called capital. After borrowing a certain amount of money (in a given or agreed time), it should be returned by the borrower to the lender the said principal of money borrowed plus the interest which is the additional amount to the principal. The rate has the "say" what is the size of the money in addition to the principal. Usually, the rate ranging from 0.5% to 15%. Some examples gave more than 15% but that depends on the case. To know the interest of money, it should be mutual to both the lender and the borrower, ( or sometimes called debtor). The borrower is the one who borrowed a certain amount of money and the lender is the one who lets his or her money be borrowed by a debtor. to know how the interest is computed, the formula is shown below:

**Business interest formula:**

**I = p*r*t**

where:

I = is the interest

p = is the principal

r = is the rate (percent)

t = is the time in years

* means multiply

### USES

Simple interest, a basic method for computing interest on loans or investments, serves several purposes in business operations:

**Borrowing and Loans**: Businesses frequently secure loans for diverse needs like expansion, equipment procurement, or covering operational costs. Simple interest simplifies interest payment calculations over the loan's duration.**Investments**: Surplus funds are often invested by businesses in interest-bearing accounts or instruments. Simple interest aids in determining the interest accrued on these investments over time.**Cash Flow Projections**: Employing simple interest helps businesses forecast cash flow more accurately. By estimating interest earnings on investments or interest payments on loans, businesses can enhance financial planning.**Short-term Financing**: For temporary financial requirements, simple interest may be employed to facilitate short-term financing. This could involve obtaining a short-term loan with simple interest to bridge cash flow gaps.**Promotional Financing**: Businesses may extend financing or credit options to customers, where simple interest calculations are useful for determining applicable interest charges.**Leasing**: Simple interest calculations are often utilized in lease agreements, particularly in equipment or vehicle leasing arrangements, to determine lease payments.**Merchant Cash Advances**: Some businesses opt for merchant cash advances, wherein they receive upfront funds in exchange for a percentage of future sales. Simple interest could be used to calculate associated fees.**Deposits**: Businesses maintain accounts with banks or financial institutions, with simple interest helping to compute interest earned on these deposits over time.

*Anna borrowed money from her friend Judy. The amount of money borrowed is $5000 and is to be paid right after six months. They both agreed to the rate of 3%. What is the interest of money to be paid by Anna to Judy?*

In the example above, notice that the time given is six months which means half a year. Therefore the time to be computed here is not six but 1/2 or 0.5 years. Here are the steps for the computation.

First, you have to write the three steps to make your computational flow. Remember the "GRS" which stands for Given, Required, and Solution (GRS).

Based on the problem above, this is the flow:

**I. Given:**

**Principal(P) = $5000**

rate (r) = 3% or 3/100 = 0.03 (this should be converted)

time (t) = 6 months or (6 months) / (12 months) = 0.5 years. This is because in one year there is 12 months.

**II. Required:**Interest (I). This is also the unknown.

**III. Solution:**This is by applying the formula by substituting the values of the given.

I = P*r*t

I = $5000*0.03*0.5

I = $75 answer

This means that Anna has $75 additional increase to the money she borrowed from her friend Judy. So this is by simply adding the principal and the interest. Hence:

**Final amount formula:**

FA = P + I

FA = P + I

**where:**

FA = final amount

P = Principal

I = Interest

**Therefore;**

**FA = P + I, or**

FA = $5000 + $75

FA = $5075

This means Anna will pay $5,075 to Judy after six months of borrowing the money for any purpose.

There are other forms of formula from

**I=p*r*t**when derived according to the required or the unknown. The unknown can be rate, time, and principal. These changes can be found by;

P = I / (r*t); when the unknown is principal

r = I/(p*t); when the unknown is rate

t = I/(p*r); when the unknown is time

By simply applying the formula the same way the example goes, you can arrive at the right solution.

**More Illustrative Examples for I (Interest) as unknown:**

**1. A man borrowed money from the bank charging 2% interest per year. The amount of money borrowed was $15,000. Find the interest of this amount after 2 years.**

**Given:**

P=$15, 000

r = 2% = 0.02

t = 2

I = ?

*(unknown)*

**Required:**I (Interest)

**Solution:**

Formula to use:

**I = Prt**

I=Prt

I=$15,000 x 0.02 x 2

I=$600

*Answer*

2. After 5 years, how much was the interest for the loan amounted to $30,000 with 3.2% interest?

**Given:**

P=$30, 000

r = 3.2% = 0.032

t = 5

I = ?

*(unknown)*

**Required:**I (Interest)

**Solution:**

Formula to use:

**I = Prt**

I=Prt

I=$30,000 x 0.032 x 5

I=$4,800

*Answer*

**3. Mario loaned an amount worth $6,500 from his friend John. They both agreed that the interest to be charged for the money is 2.3% good for 3. years and 6 months. How much would be the interest on the money borrowed by Mario from John?**

**Given:**

P=$6,500

r = 2.3% = 0.023

t = 3.5

I = ?

*(unknown)*

**Required:**I (Interest)

**Solution:**

Formula to use:

**I = Prt**

I=Prt

I=$6,500 x 0.023 x 3.5

I=$523.25

*Answer*

4. Kaye lends her money to a friend Marty. Marty agreed that he would pay the interest as 5% after 6 months. How much would be the interest if Marty borrowed $5,000?

**Given:**

P=$5,000

r = 5% = 0.05

t = 0.5

I = ?

*(unknown)*

**Required:**I (Interest)

**Solution:**

Formula to use:

**I = Prt**

I=Prt

I=$5,000 x 0.05 x 0.5

I=$125

*Answer*

**Given:**

P=$10,000

r = 4% = 0.04

t = 3

I = ?

*(unknown)*

**Required:**I (Interest)

**Solution:**

Formula to use:

**I = Prt**

I=Prt

I=$10,000 x 0.04 x 3

I=$1,200

*Answer*

6. Imagine that an ABC Company borrows $10,000 from a bank with a straightforward interest rate of 8% annually to buy new equipment for their manufacturing plant. They have to repay the loan after one year. How much interest will ABC Company have to pay by the end of the loan term?

Solution: Initial loan amount (P) = $10,000 Yearly interest rate (R) = 8% Duration of the loan (T) = 1 year

To calculate the interest, we use this formula:

$Interest=Principal×Rate×Time$

**I = Prt**

Plugging in the given values: $$

$$

Therefore, ABC Company will need to pay a total interest of $800 by the end of the loan term.

This implies that ABC Company has to repay the initial loan amount of $10,000 plus the $800 interest, resulting in a total repayment amount of $10,800.

**More Illustrative Examples for r(rate) as unknown:**

**1**1. Find the interest rate for the $6,000 money borrowed after 3 years with $600 interest.

**Given:**

**P = $6,000**

**Required:**r (rate)

**Solution:**

**Formula to use: r = I /(pt)**;

*Derived from I=prt*

*substitute the value of p,I, and t respectively*

r = 0.0333 or

r = 0.0333 x 100%

r = 3.33%

*Answer*

**2. A lending company puts an interest of $700 for the $10,000 amount for the borrower in 2 years. What is the interest rate charged by the company to the borrower?**

**Given:**

**P = $10,000**

**Required:**r (rate)

**Solution:**

**Formula to use:**

**r = I /(pt)**;

*Derived from I=prt*

*substitute the value of p,I, and t respectively*

r = 0.035 or

r = 0.035 x 100%

r = 3.5%

*Answer*

**Given:**

**P = $50,000**

**Required:**r (rate)

**Solution:**

**Formula to use:**

**r = I /(pt)**;

*Derived from I=prt*

*substitute the value of p,I, and t respectively*

r = 0.0154 or

r = 0.0154 x 100%

r = 1.54%

*Answer*

*4*. How much would be the interest rate if you have $6,480 as interest on your $12000 money after 6 years?

**Given:**

**P = $12,000**

**Required:**r (rate)

**Solution:**

**Formula to use:**

**r = I /(pt)**;

*Derived from I=prt*

*substitute the value of p,I, and t respectively*

r = 0.09 or

r = 0.09 x 100%

r = 9%

*Answer*

**Given:**

**P = $16,500**

**Required:**r (rate)

**Solution:**

**Formula to use:**

**r = I /(pt)**;

*Derived from I=prt*

*substitute the value of p, I, and t respectively*

r = 0.0140 or

r = 0.0140 x 100%

r = 1.4 %

*Answer*

6. XYZ Company invests $5,000 in a savings account. After one year, they receive $5,300, including the interest earned. What is the annual simple interest rate XYZ Company earned on their investment?

**Solution:**
Initial investment amount (P) = $5,000
Total amount after one year (A) = $5,300

To find the interest earned, we subtract the initial investment from the total amount:

$Interest=TotalAmount−InitialInvestment$ Interest = $5,300 - $5,000 Interest = $300

Now, to find the annual interest rate, we can use the formula:

$Interest=Principal×Rate×Time$

Since the rate is unknown, we can rearrange the formula to solve for the rate.

$Rate=\frac{Interest}{Principal\times Tim\mathrm{e}}$

Plugging in the values in dollars ($):

Therefore, XYZ Company earned a simple interest rate of 6% annually on their investment.

**More Illustrative Examples for Time(t) as unknown:**

1. Consider ABC Company's investment of $8,000 in a savings account with a simple interest rate of 4% per year. Over time, the investment grows to $8,320, including the interest earned. How long did it take for ABC Company's investment to reach this amount?

**Solution:**

Initial investment amount= $8,000

Total amount after some time = $8,320

Annual interest rate= 4%

To determine the time taken for the investment to grow, we can use the formula for simple interest:

$\mathrm{Time=\frac{Interest}{Principal\times Rate}}$

First, we need to calculate the interest earned in dollars:

$=TotalAmount−InitialInvestment$ Interest = $8,320 - $8,000

**Interest **= $320

Now, let's calculate the time:

**Solution:**

Calculate the duration (Time):

$$

**Interest** = $6,700 - $6,500

**Interest **= $200

Calculate the time:

$Time=\frac{Interest}{Principal\times Rate}$

$Therefore, it took approximately 1.03 years for Mr. Yu Corporation's investment to grow to $6,700.$

**Solution:**

Initial investment amount= $12,000

Total amount after some time = $13,200

Annual interest rate= 5%

Calculate the interest earned (in dollars $):

$=TotalAmount−InitialInvestment$

**Interest** = $13,200 - $12,000

**Interest** = $1,200

Calculating the duration in years.

$Time=\frac{Interest}{Principal\times Rate}$

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