Course outline
Module 1
Module 1: What Is Interest?
What Is Interest?
Knowledge check
Q1. What is interest in the context of borrowing or saving money?
- A. A fee charged for opening a bank account
- B. The cost of borrowing money or the earnings from lending or saving money, expressed as a percentage of the amount ✓
- C. The total amount of money you deposit in a bank
- D. A tax paid to the government on all income
Why: Interest is the cost of using someone else's money (when borrowing) or the reward for letting a bank or lender use your money (when saving), typically expressed as a percentage of the principal amount.
Q2. If you deposit $1,000 in a savings account that pays 5% simple interest per year, how much interest will you earn after one year?
- A. $5
- B. $50 ✓
- C. $500
- D. $1,050
Why: 5% of $1,000 is calculated as 0.05 × $1,000 = $50. This $50 is the interest earned over one year.
Q3. What is the principal in a loan or investment?
- A. The interest rate applied to the loan
- B. The final amount owed after all interest is added
- C. The original amount of money borrowed or invested ✓
- D. The fee charged by the bank for processing the loan
Why: The principal is the starting sum of money, the original amount borrowed or invested, on which interest is calculated.
Q4. Which of the following best describes simple interest?
- A. Interest calculated only on the original principal amount ✓
- B. Interest calculated on both the principal and previously earned interest
- C. Interest that changes randomly each month
- D. Interest that is paid only at the end of a loan's full term
Why: Simple interest is calculated only on the original principal. Unlike compound interest, it does not earn interest on previously accumulated interest.
Q5. Why is interest important to understand before saving or borrowing money?
- A. It determines how much you must pay in taxes each year
- B. It affects how much your money grows when saving and how much you pay over time when borrowing ✓
- C. It only matters for people who work in banking
- D. It is the same for every financial product, so it does not need comparison
Why: Interest directly determines how savings grow and how much debt costs over time, so understanding it helps people make better financial decisions.
Module 2
Module 2: Simple Interest Explained
Simple Interest Explained
Knowledge check
Q1. What is the formula for simple interest?
- A. I = P × r × t ✓
- B. I = P × (1 + r)^t
- C. I = P + r + t
- D. I = P ÷ r × t
Why: Simple interest is calculated by multiplying the principal (P), the annual interest rate (r), and the time in years (t). Option B describes compound interest, not simple interest.
Q2. If you deposit $1,000 at a simple interest rate of 5% per year, how much interest do you earn after 3 years?
- A. $50
- B. $150 ✓
- C. $165
- D. $1,150
Why: Using I = P × r × t: $1,000 × 0.05 × 3 = $150. Option C would result from compound interest, and option D is the total balance, not the interest earned.
Q3. Which of the following best describes simple interest?
- A. Interest earned on both the principal and previously earned interest
- B. Interest calculated only on the original principal amount ✓
- C. Interest that changes randomly each year
- D. Interest that is paid only at the end of the loan term
Why: Simple interest is calculated only on the original principal, so it does not earn interest on previously accumulated interest. That feature belongs to compound interest.
Q4. A loan of $2,000 has a simple interest rate of 4% per year. What is the total amount owed after 2 years, including interest?
- A. $2,080
- B. $2,160 ✓
- C. $2,400
- D. $2,040
Why: Interest is $2,000 × 0.04 × 2 = $160. Adding this to the principal gives $2,000 + $160 = $2,160.
Q5. Why does simple interest grow more slowly than compound interest over long periods?
- A. Because the interest rate decreases each year
- B. Because interest is never added to the principal, so it does not earn further interest ✓
- C. Because simple interest is only paid once
- D. Because simple interest uses a smaller time period
Why: With simple interest, earned interest is never reinvested into the principal, so the base for each year's calculation stays the same. Compound interest reinvests earnings, causing faster growth over time.
Module 3
Module 3: How Compounding Works
How Compounding Works
Knowledge check
Q1. What is compound interest?
- A. Interest calculated only on the original principal amount
- B. Interest calculated on both the original principal and previously earned interest ✓
- C. A fixed fee charged by a bank each year
- D. Interest that decreases over time as the balance grows
Why: Compound interest is earned on both the initial principal and on the interest that has already been added to the balance, so the amount grows faster over time than simple interest.
Q2. If you invest $1,000 at 10% annual interest compounded once per year, how much will you have after 2 years?
- A. $1,200
- B. $1,210 ✓
- C. $1,100
- D. $1,020
Why: After year 1 you have $1,000 x 1.10 = $1,100. In year 2 you earn 10% on $1,100, giving $1,100 x 1.10 = $1,210. Simple interest would only give $1,200.
Q3. Which factor causes an investment to grow the MOST through compounding?
- A. A shorter investment period
- B. A smaller starting amount
- C. A longer investment period ✓
- D. Withdrawing interest each year
Why: Compounding works exponentially, so the longer money stays invested, the more the interest itself earns interest. Time is one of the most powerful factors in compound growth.
Q4. Which compounding frequency would produce the highest ending balance, all else being equal?
- A. Annually
- B. Semi-annually
- C. Quarterly
- D. Daily ✓
Why: The more often interest is compounded, the sooner interest starts earning its own interest. Daily compounding therefore yields the highest balance among these options, though the difference grows smaller as frequency increases.
Q5. Using the rule of 72, approximately how many years will it take for an investment to double at an annual return of 6%?
- A. 6 years
- B. 12 years ✓
- C. 72 years
- D. 24 years
Why: The rule of 72 estimates doubling time by dividing 72 by the annual interest rate. 72 divided by 6 equals 12, so the investment roughly doubles in 12 years.
Module 4
Module 4: The Compound Interest Formula
The Compound Interest Formula
Knowledge check
Q1. In the compound interest formula A = P(1 + r/n)^(nt), what does the variable P represent?
- A. The total amount after interest is applied
- B. The principal, or initial amount of money invested or borrowed ✓
- C. The annual interest rate as a decimal
- D. The number of years the money is invested
Why: P stands for the principal, the starting sum of money. A is the final amount, r is the rate, n is compounding periods per year, and t is time in years.
Q2. If $1,000 is invested at 5% annual interest compounded once per year, how much is it worth after 1 year?
- A. $1,005.00
- B. $1,050.00 ✓
- C. $1,500.00
- D. $1,025.00
Why: Using A = P(1 + r/n)^(nt) with P = 1000, r = 0.05, n = 1, t = 1 gives 1000(1.05) = 1050. Interest earned is $50.
Q3. Which variable in the compound interest formula represents the number of times interest is compounded per year?
Why: n is the number of compounding periods per year, such as 1 for annual, 4 for quarterly, or 12 for monthly compounding.
Q4. Using the formula A = P(1 + r/n)^(nt), what is the value of (1 + r/n) when the annual rate r is 8% and interest is compounded quarterly (n = 4)?
- A. 1.08
- B. 1.02 ✓
- C. 1.20
- D. 1.32
Why: Divide the rate by the number of periods: r/n = 0.08/4 = 0.02, so 1 + r/n = 1.02.
Q5. Why does compounding more frequently (for example, monthly instead of annually) lead to a larger final amount?
- A. The principal is reduced with each compounding period
- B. Interest is calculated and added to the balance more often, so interest starts earning its own interest sooner ✓
- C. The interest rate automatically increases with each period
- D. Time is counted differently when compounding is more frequent
Why: With more frequent compounding, interest is added to the balance earlier, and that added interest then earns interest in subsequent periods, producing a higher total.
Module 5
Module 5: Compounding Frequency and Effective Rates
Compounding Frequency and Effective Rates
Knowledge check
Q1. What does the compounding frequency of an interest rate refer to?
- A. The total amount of money invested at the start
- B. How often interest is calculated and added to the principal ✓
- C. The length of time the money is held in the account
- D. The percentage of profit the bank keeps as a fee
Why: Compounding frequency is the number of times per year that earned interest is calculated and added to the principal, so that future interest is earned on the larger balance.
Q2. An account pays 12% annual interest compounded monthly. What is the monthly interest rate?
- A. 12%
- B. 6%
- C. 1% ✓
- D. 0.12%
Why: With monthly compounding there are 12 periods per year, so the periodic rate is the annual rate divided by 12: 12% / 12 = 1% per month.
Q3. Which account would grow the most over one year, assuming the same nominal annual rate?
- A. Interest compounded annually
- B. Interest compounded quarterly
- C. Interest compounded monthly ✓
- D. Interest compounded once every two years
Why: More frequent compounding means interest is added to the balance more often, so interest earns interest sooner. Monthly compounding gives the highest growth among these options.
Q4. What is the effective annual rate (EAR) of a 10% nominal rate compounded annually?
- A. 9%
- B. 10% ✓
- C. 10.25%
- D. 11%
Why: When interest compounds only once per year, the effective annual rate equals the nominal rate, so the EAR is exactly 10%.
Q5. Why is the effective annual rate (EAR) useful when comparing financial products?
- A. It always equals the nominal rate, so it simplifies calculations
- B. It shows the true yearly return including the effect of compounding, allowing fair comparison ✓
- C. It removes the need to consider fees and taxes
- D. It guarantees the account balance will never decrease
Why: The EAR reflects the real annual growth after compounding, so products with different compounding frequencies can be compared on an equal basis.
Module 6
Module 6: The Power of Time and Early Investing
The Power of Time and Early Investing
Knowledge check
Q1. What is the main difference between simple interest and compound interest?
- A. Simple interest is calculated only on the original principal, while compound interest is calculated on the principal plus previously earned interest.
- B. Simple interest grows faster than compound interest over long periods.
- C. Compound interest is only paid once at the end of the loan term.
- D. Simple interest applies only to savings accounts, while compound interest applies only to loans.
Q2. If you invest $1,000 at a 5% annual interest rate compounded annually, how much will you have after 2 years?
- A. $1,050.00
- B. $1,100.00
- C. $1,102.50
- D. $1,110.00
Q3. Which factor has the greatest impact on the growth of an investment due to compounding?
- A. The amount of money you start with
- B. The length of time the money is invested
- C. The type of bank holding the account
- D. The number of withdrawals you make
Q4. Two friends invest $5,000 at the same 7% annual return. Alex starts at age 25 and Ben starts at age 35, both holding until age 65. Why does Alex end up with significantly more money?
- A. Alex receives a higher interest rate from the bank.
- B. Alex's money has an extra 10 years to compound, allowing earnings to generate their own earnings.
- C. Ben pays more in fees because he starts later.
- D. Alex invests more total dollars over the period.
Q5. Using the Rule of 72, approximately how many years will it take for an investment to double at an annual return of 6%?
- A. 6 years
- B. 10 years
- C. 12 years
- D. 72 years
Module 7
Module 7: Applying Compound Interest in Real Life
Applying Compound Interest in Real Life
Knowledge check
Q1. If you deposit $1,000 in a savings account that pays 5% interest compounded annually, how much will you have after 1 year?
- A. $1,005
- B. $1,050 ✓
- C. $1,500
- D. $1,055
Why: Compound interest adds interest to the principal. 5% of $1,000 is $50, so the balance after one year is $1,000 + $50 = $1,050.
Q2. What is the main difference between simple interest and compound interest?
- A. Simple interest is paid only on the original principal, while compound interest is paid on the principal plus previously earned interest. ✓
- B. Simple interest grows faster than compound interest over time.
- C. Compound interest is only used for loans, while simple interest is used for savings.
- D. Simple interest changes every month, while compound interest stays fixed.
Why: Compound interest earns interest on accumulated interest as well as the original principal, which causes faster growth over time compared to simple interest.
Q3. Which factor has the greatest positive effect on the growth of an investment over long periods?
- A. Starting with a smaller principal amount
- B. Withdrawing interest every year
- C. Time spent invested ✓
- D. Changing banks frequently
Why: Because compound interest builds on itself, the longer money stays invested, the more dramatically it grows. Time is one of the most powerful factors in compounding.
Q4. If a credit card charges 18% annual interest compounded monthly on an unpaid balance, what happens to the debt over time?
- A. The debt stays the same as long as you make minimum payments.
- B. The debt shrinks because interest is subtracted from the balance.
- C. The debt grows because interest is charged on both the original balance and previously added interest. ✓
- D. The debt only increases when new purchases are made.
Why: Compound interest works against borrowers as well. Unpaid interest is added to the balance, and future interest is calculated on that larger amount, so the debt grows faster.
Q5. Using the rule of 72, approximately how many years will it take for an investment earning 8% annual compound interest to double?
- A. 6 years
- B. 9 years ✓
- C. 12 years
- D. 24 years
Why: The rule of 72 estimates doubling time by dividing 72 by the annual interest rate. 72 divided by 8 equals 9 years.