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# Financial management - simple interest

The formula A=P×(1+r×t)A=P×(1+r×t) is used to calculate the total amount AA accumulated after applying simple interest. This formula combines the principal amount PP with the interest earned over time, where the interest is calculated simply based on the original principal.

### Formula Explanation

• AA: The total amount after interest.

• PP: The principal amount (initial investment or loan amount).

• rr: The annual interest rate (expressed as a decimal).

• tt: The time the money is invested or borrowed for, in years.

### Example 1: Investment

Problem: You invest \$1,000 in a savings account with a simple interest rate of 5% per year for 3 years. What will be the total amount in the account after 3 years?

Solution:

1. Identify the values:

• P=1000P=1000

• r=0.05r=0.05 (5% as a decimal)

• t=3t=3 years

2. Plug these values into the formula:

A=P×(1+r×t)A=P×(1+r×t)A=1000×(1+0.05×3)A=1000×(1+0.05×3)

3. Calculate inside the parentheses:

1+0.05×3=1+0.15=1.151+0.05×3=1+0.15=1.15

4. Multiply by the principal amount:

A=1000×1.15=1150A=1000×1.15=1150

So, the total amount in the account after 3 years will be \$1,150.

### Example 2: Loan

Problem: You borrow \$2,500 with a simple interest rate of 4% per year for 5 years. What will be the total amount to be repaid?

Solution:

1. Identify the values:

• P=2500P=2500

• r=0.04r=0.04 (4% as a decimal)

• t=5t=5 years

2. Plug these values into the formula:

A=P×(1+r×t)A=P×(1+r×t)A=2500×(1+0.04×5)A=2500×(1+0.04×5)

3. Calculate inside the parentheses:

1+0.04×5=1+0.20=1.201+0.04×5=1+0.20=1.20

4. Multiply by the principal amount:

A=2500×1.20=3000A=2500×1.20=3000

So, the total amount to be repaid after 5 years will be \$3,000.

### Key Points

• Simple Interest Calculation: The formula A=P×(1+r×t)A=P×(1+r×t) straightforwardly computes the total amount by combining the principal with the interest accumulated over time.

• No Compounding: Simple interest does not compound; it only considers the initial principal amount for calculating interest.

• Conversion: Always convert the interest rate into a decimal (e.g., 6% = 0.06) and ensure the time period is in years to use the formula accurately.

Example 1: Savings Account

Problem: You deposit \$2,000 into a savings account that offers a simple interest rate of 3% per year. What will be the total amount in the account after 4 years?

Solution:

1. Identify the values:

• Principal amount P=2000P=2000

• Annual interest rate r=0.03r=0.03 (3% as a decimal)

• Time t=4t=4 years

2. Use the formula for simple interest to find the total amount AA:

A=P×(1+r×t)A=P×(1+r×t)A=2000×(1+0.03×4)A=2000×(1+0.03×4)

3. Calculate inside the parentheses:

1+0.03×4=1+0.12=1.121+0.03×4=1+0.12=1.12

4. Multiply by the principal amount:

A=2000×1.12=2240A=2000×1.12=2240

So, the total amount in the account after 4 years will be \$2,240.

### Example 2: Car Loan

Problem: You take out a car loan of \$10,000 at a simple interest rate of 6% per year. How much total interest will you pay over a period of 3 years?

Solution:

1. Identify the values:

• Principal amount P=10000P=10000

• Annual interest rate r=0.06r=0.06 (6% as a decimal)

• Time t=3t=3 years

2. Calculate the interest using the simple interest formula:

I=P×r×tI=P×r×tI=10000×0.06×3I=10000×0.06×3

3. Perform the calculation:

I=10000×0.18=1800I=10000×0.18=1800

So, the total interest paid over 3 years will be \$1,800.

### Example 3: Fixed Deposit

Problem: You invest \$5,000 in a fixed deposit for 2 years at a simple interest rate of 8% per year. What will be the total amount at the end of the investment?

Solution:

1. Identify the values:

• Principal amount P=5000P=5000

• Annual interest rate r=0.08r=0.08 (8% as a decimal)

• Time t=2t=2 years

2. Use the formula for the total amount AA:

A=P×(1+r×t)A=P×(1+r×t)A=5000×(1+0.08×2)A=5000×(1+0.08×2)

3. Calculate inside the parentheses:

1+0.08×2=1+0.16=1.161+0.08×2=1+0.16=1.16

4. Multiply by the principal amount:

A=5000×1.16=5800A=5000×1.16=5800

So, the total amount at the end of 2 years will be \$5,800.

### Example 4: Short-Term Loan

Problem: You borrow \$1,200 for 6 months at a simple interest rate of 9% per year. How much total interest will you pay, and what will be the total repayment amount?

Solution:

1. Identify the values:

• Principal amount P=1200P=1200

• Annual interest rate r=0.09r=0.09 (9% as a decimal)

• Time t=0.5t=0.5 years (6 months)

2. Calculate the interest using the simple interest formula:

I=P×r×tI=P×r×tI=1200×0.09×0.5I=1200×0.09×0.5

3. Perform the calculation:

I=1200×0.045=54I=1200×0.045=54

4. Calculate the total repayment amount:

A=P+IA=P+IA=1200+54=1254A=1200+54=1254

So, the total interest paid will be \$54, and the total repayment amount will be \$1,254.

### Summary

These examples illustrate how to apply the simple interest formula in different scenarios. Remember:

• Interest Calculation: Use I=P×r×tI=P×r×t to find the interest amount.

• Total Amount: Use A=P×(1+r×t)A=P×(1+r×t) to find the total amount after interest.

• Principal: Always ensure that time is expressed in years and interest rates in decimal form for accurate calculations.