Example 1: Understanding Simple Interest
Imagine you lend your friend $1,000 at a simple interest rate of 5% per year. Each year, your friend will owe you $50 in interest, calculated as 5% of $1,000. After one year, your friend will owe you $1,050 total (the original $1,000 principal plus $50 interest). If the loan continues for another year, the interest for the second year will still be $50, and the total amount owed will be $1,100.
Example 2: Understanding Compound Interest
Consider you invest $1,000 in a savings account with an annual compound interest rate of 5%. At the end of the first year, your investment grows by $50 (5% of $1,000), making it $1,050. In the second year, the interest is calculated on $1,050, resulting in $52.50 interest. So, at the end of the second year, your investment will be $1,102.50.
Example 3: Principal in Loans
If you take out a loan of $5,000, the $5,000 is the principal amount. Suppose the loan has an interest rate of 4% per year. Initially, the interest for the first year would be $200 (4% of $5,000). If you make an additional payment of $1,000 towards the principal, your new principal becomes $4,000, and the interest for the next year will be $160 (4% of $4,000).
Example 4: Annuity for Retirement
A retiree purchases a fixed annuity with a lump sum of $100,000 that pays $500 per month for life. This fixed annuity provides the retiree with a predictable income stream. In contrast, if the retiree had purchased a variable annuity, the monthly payments could fluctuate based on the performance of the underlying investments, potentially offering higher returns but also carrying more risk.
Example 5: Amortization in Mortgages
Consider a 30-year mortgage of $200,000 with an interest rate of 4% per year. An amortization schedule will show that in the early years, a larger portion of your monthly payment goes towards interest rather than the principal. For instance, the first payment might allocate $667 towards interest and $288 towards the principal. Over time, as the principal decreases, the interest portion of the payments reduces, and more goes towards the principal, gradually paying off the loan.
Example 6: Amortization of Intangible Assets
A company purchases a patent for $100,000, which has a useful life of 10 years. Using straight-line amortization, the company would spread the cost of the patent evenly over 10 years. Each year, the company would expense $10,000 ($100,000 divided by 10), reflecting the annual amortization cost on its financial statements.