Simple and Compound Interest- Practice Problems

What This Article Covers

You'll get practice problems with solutions for both simple and compound interest. No theory dumps. No lengthy explanations. Just problems you can actually solve, followed by the answers so you can check your work.

If you don't know the formulas yet, scroll down. I included them. If you do know them, skip ahead to the problems.

The Formulas You Need

These are the only two formulas that matter. Memorize them or write them down. You'll use them for every problem below.

Simple Interest

SI = P × R × T ÷ 100

Where:

• SI = Simple Interest
• P = Principal (the starting amount)
• R = Rate per year (as a percentage)
• T = Time (in years)

Total Amount = P + SI

Compound Interest

A = P(1 + R÷100)^T

Where:

• A = Total Amount after T years
• P = Principal
• R = Annual interest rate
• T = Time in years

Compound Interest = A - P

Simple Interest Practice Problems

These problems use the simple interest formula. Calculate the interest earned or the total amount.

Problem 1

You deposit $5,000 at a rate of 4% per year for 3 years. What's the simple interest?

Solution:

SI = 5000 × 4 × 3 ÷ 100

SI = $600

You'll earn $600 in interest. The total in your account will be $5,600.

Problem 2

A loan of $2,500 accumulates $375 in simple interest over 3 years. What's the annual interest rate?

Solution:

Using SI = P × R × T ÷ 100

375 = 2500 × R × 3 ÷ 100

375 = 7500R ÷ 100

375 = 75R

R = 5%

The rate is 5% per year.

Problem 3

At what rate will $8,000 grow to $9,200 in 3 years using simple interest?

Solution:

Interest earned = 9200 - 8000 = $1,200

1200 = 8000 × R × 3 ÷ 100

1200 = 240R

R = 5%

You need a 5% annual rate.

Problem 4

How long will it take $10,000 to earn $2,000 in simple interest at 5% per year?

Solution:

2000 = 10000 × 5 × T ÷ 100

2000 = 500T

T = 4 years

It takes 4 years.

Compound Interest Practice Problems

These problems use the compound interest formula. Pay attention to whether interest is compounded annually, semi-annually, or quarterly.

Problem 5

You invest $10,000 at 6% compound interest for 5 years. What's the total amount?

Solution:

A = P(1 + R÷100)^T

A = 10000(1 + 6÷100)^5

A = 10000(1.06)^5

A = 10000 × 1.3382

A = $13,382.26

Your investment grows to $13,382.26. The compound interest earned is $3,382.26.

Problem 6

Calculate the compound interest on $6,000 at 8% per year for 2 years.

Solution:

A = 6000(1 + 8÷100)^2

A = 6000(1.08)^2

A = 6000 × 1.1664

A = $6,998.40

Compound Interest = 6998.40 - 6000 = $1,998.40

You earn $1,998.40 in interest.

Problem 7

What principal will grow to $25,000 in 4 years at 5% compound interest?

Solution:

25000 = P(1.05)^4

25000 = P × 1.2155

P = 25000 ÷ 1.2155

P = $20,567.58

You need to invest about $20,568 to reach $25,000 in 4 years.

Problem 8

At what rate will $4,000 double in 5 years with annual compounding?

Solution:

8000 = 4000(1 + R÷100)^5

2 = (1 + R÷100)^5

2^(1/5) = 1 + R÷100

1.1487 = 1 + R÷100

R = 14.87%

You need approximately 14.87% annual rate to double your money in 5 years.

Semi-Annual and Quarterly Compounding

Most compound interest problems assume annual compounding. But sometimes you need to adjust for more frequent compounding periods.

Problem 9

Calculate the amount on $5,000 at 8% per year for 2 years, compounded half-yearly.

Solution:

When compounded semi-annually:

• Rate per period = 8% ÷ 2 = 4%
• Number of periods = 2 × 2 = 4

A = 5000(1 + 4÷100)^4

A = 5000(1.04)^4

A = 5000 × 1.1699

A = $5,849.29

Problem 10

Find the compound interest on $12,000 at 6% for 1.5 years, compounded quarterly.

Solution:

• Rate per quarter = 6% ÷ 4 = 1.5%
• Number of quarters = 1.5 × 4 = 6

A = 12000(1.015)^6

A = 12000 × 1.0937

A = $13,124.40

Compound Interest = 13124.40 - 12000 = $1,124.40

Simple vs Compound Interest Comparison

Here's how the two methods differ side by side using the same inputs.

Compound interest always wins over time. The gap widens the longer you hold the money.

Common Mistakes to Avoid

• Mixing up the formulas. Simple interest uses division by 100. Compound interest uses multiplication by (1 + rate). Don't swap them.
• Forgetting to annualize the rate. If interest is 12% per year but compounds monthly, use 1% per month. Not 12%.
• Using time in the wrong units. If the rate is annual but the time is in months, convert everything to years first.
• Rounding too early. Keep at least 4 decimal places during calculations. Round only at the final answer.
• Confusing total amount with interest. The formula gives you the total amount. Subtract the principal to get the interest earned.

How to Solve Any Interest Problem

Follow these steps for every problem you encounter.

Step 1: Identify the Variables

Write down P, R, and T from the problem. Check if it's simple or compound interest.

Step 2: Choose the Right Formula

Simple interest: SI = P × R × T ÷ 100

Compound interest: A = P(1 + R÷100)^T

Step 3: Plug in the Numbers

Substitute your values. Double-check you've used the correct rate and time period.

Step 4: Calculate

Use a calculator for compound interest. For simple interest, basic arithmetic works.

Step 5: Answer the Question

Some problems ask for total amount. Others ask for interest earned. Make sure you're giving what was requested.

Quick Reference Cheat Sheet

• Simple Interest: Interest is always calculated on the original principal. It never changes.
• Compound Interest: Interest is calculated on the accumulated balance. It grows over time.
• Annual compounding: One period per year
• Semi-annual compounding: Two periods per year
• Quarterly compounding: Four periods per year
• Monthly compounding: Twelve periods per year

That's 10 practice problems with full solutions. You now have enough material to practice simple and compound interest until these formulas become automatic. 📊