Simple Interest Calculations Explained

Sure, I can help you understand solved exercises related to simple interest in English.

Let’s start with some basic concepts about simple interest:

Simple interest is a type of interest that is calculated only on the initial principal amount of a loan or deposit, without taking into account any additional contributions or withdrawals made during the term of the investment or loan. The formula for calculating simple interest is:

$I = P \times r \times t$

Where:

• $I$ is the interest earned or paid,
• $P$ is the principal amount (the initial amount of money),
• $r$ is the annual interest rate (expressed as a decimal),
• $t$ is the time period (in years).

Now, let’s go through some solved exercises related to simple interest:

Exercise 1: Calculate the simple interest earned on a principal amount of $2000 at an annual interest rate of 5% for 3 years.

Solution:
P = $2000
$r = 5\% = 0.05$
$t = 3 \text{ years}$

Using the formula $I = P \times r \times t$:
I = $2000 \times 0.05 \times 3 = $300

So, the simple interest earned is $300.

Exercise 2: Find the total amount accrued if a principal amount of $5000 is invested at an annual interest rate of 8% for 5 years.

Solution:
P = $5000
$r = 8\% = 0.08$
$t = 5 \text{ years}$

First, calculate the simple interest using the formula $I = P \times r \times t$:
I = $5000 \times 0.08 \times 5 = $2000

Next, add the interest to the principal to find the total amount:
\text{Total amount} = P + I = $5000 + $2000 = $7000

So, the total amount accrued is $7000.

Exercise 3: Determine the principal amount if $120 interest is earned on an investment at an annual interest rate of 6% for 4 years.

Solution:
I = $120
$r = 6\% = 0.06$
$t = 4 \text{ years}$

We need to rearrange the formula $I = P \times r \times t$ to solve for $P$:
P = \frac{I}{r \times t} = \frac{$120}{0.06 \times 4} = $500

So, the principal amount is $500.

These exercises illustrate how simple interest is calculated and how it can be used to find the interest earned, total amount accrued, or principal amount in various financial scenarios. Understanding these concepts can be helpful in personal finance management and investment decision-making.

Certainly! Let’s delve deeper into the concept of simple interest and explore additional solved exercises to enhance your understanding.

Understanding Simple Interest:

Simple interest is a fundamental concept in finance that is used to calculate the interest earned or paid on a principal amount over a specific period. Unlike compound interest, which takes into account both the principal and accumulated interest, simple interest is based solely on the original principal amount.

The formula for calculating simple interest is straightforward:

$I = P \times r \times t$

Where:

• $I$ is the interest earned or paid,
• $P$ is the principal amount (the initial amount of money),
• $r$ is the annual interest rate (expressed as a decimal),
• $t$ is the time period (in years).

Solved Exercises:

Let’s solve some more exercises to reinforce your understanding of simple interest calculations:

Exercise 4: An amount of $3000 is borrowed at an annual interest rate of 7%. Calculate the total amount to be repaid after 2 years.

Solution:
P = $3000
$r = 7\% = 0.07$
$t = 2 \text{ years}$

Using the simple interest formula:
I = P \times r \times t = $3000 \times 0.07 \times 2 = $420

The total amount to be repaid is the principal plus the interest:
\text{Total amount} = P + I = $3000 + $420 = $3420

So, the borrower needs to repay $3420 in total after 2 years.

Exercise 5: If $800 is invested at an annual interest rate of 4%, calculate the time required for the investment to earn $128 in interest.

Solution:
P = $800
$r = 4\% = 0.04$
I = $128

To find the time period $t$, rearrange the simple interest formula:
t = \frac{I}{P \times r} = \frac{$128}{$800 \times 0.04} = \frac{4}{25} \text{ years}

Converting the time to months (1 year = 12 months):
$t = \frac{4}{25} \times 12 = \frac{48}{25} \text{ months} \approx 1.92 \text{ months}$

So, it will take approximately 1 year and 11 months for the investment to earn $128 in interest.

Exercise 6: A loan of $5000 is repaid with an interest of $600 after 3 years. Calculate the annual interest rate.

Solution:
P = $5000
I = $600
$t = 3 \text{ years}$

To find the annual interest rate $r$, rearrange the simple interest formula:
r = \frac{I}{P \times t} = \frac{$600}{$5000 \times 3} = \frac{4}{25} = 0.16

Convert the decimal to a percentage:
$r = 0.16 \times 100\% = 16\%$

So, the annual interest rate on the loan is 16%.

Exercise 7: An investment earns $240 in interest after 5 years at an annual interest rate of 6%. Calculate the principal amount.

Solution:
I = $240
$r = 6\% = 0.06$
$t = 5 \text{ years}$

To find the principal amount $P$, rearrange the simple interest formula:
P = \frac{I}{r \times t} = \frac{$240}{0.06 \times 5} = \frac{240}{0.3} = $800

So, the principal amount invested was $800.

These exercises cover various scenarios involving simple interest calculations, including finding the total amount repaid, the time required to earn a certain interest, determining the annual interest rate, and calculating the principal amount. Mastering these concepts can empower you to make informed financial decisions and manage your investments effectively.