Simple Interest

Simple Interest

Understanding Simple Interest

• When you deposit money into a savings account, the bank pays you for using your money.
• The amount you deposit is called the principal.
• The amount the bank pays you is called interest.
• If you borrow money, you pay back the principal plus interest.
• Interest is a percentage, also known as the interest rate.
• Example: Mortgage on a house.
  • If you borrow $300,000$ to buy a house, you might pay back $400,000$ or $500,000$ over time due to interest.
  • The bank charges an interest rate (e.g., $7.9\%$, also referred to as $7.9\%$ interest).
• To calculate the interest amount, convert the percentage to a decimal, then multiply by the principal.

Simple vs. Compound Interest

• In simple interest, interest is added to the principal only at the end of the specified time period.
• In real life, banks usually calculate compound interest, where interest is added to the principal at regular intervals (e.g., monthly or daily).
• Credit Cards
  • Interest is calculated if you miss the payment deadline.
  • Example: If you buy something for $100$ on May 1st and don't pay it off by May 31st, interest starts accruing on June 1st.

Example 1: Calculating Simple Interest

• Problem: How much interest does a principal of $2,000$ earn in a year if the yearly interest rate is $5\%$.
• Solution:
  • The interest is simply $5\%$ of $2,000$, which is $100$ dollars.
  • Convert $5\%$ to a decimal: $\frac{5}{100} = 0.05$.
  • $I$ (Interest Rate) = $0.05$. $P$ (Principal) = $2,000$.
  • Multiply $0.05 \times 2,000 = 100$.

Example 2: Calculating Loan Payback

• Problem: You get a $3,000$ loan with an annual interest rate of $8.5\%$. You pay the loan back after three years. How much do you have to pay back?
• Solution:
  • Convert $8.5\%$ to a decimal: $\frac{8.5}{100} = 0.085$.
  • Multiply the interest rate by the number of years: $0.085 \times 3 = 0.255$.
  • Multiply this result by the principal to find the total interest: $0.255 \times 3,000 = 765$.
  • Add the interest to the principal to find the total amount to pay back: $3,000 + 765 = 3,765$.

Simple Interest Formula

• $I = PRT$, where:
  • $I$ = Interest
  • $P$ = Principal
  • $R$ = Interest Rate
  • $T$ = Time
• The time component can be tricky and might require converting between months and years to match the interest rate's units.

Calculating Interest and Total Amount

• Calculate the interest and the total amount to be paid back on these investments.
  • P (Principal) = $5,000, I (Interest) = 3%, Time = 1 year
    • 5,000 * 0.03 * 1 = 150
    • Total to withdraw = 5,000 + 150 = 5,150
  • P = 3,500, I = 4.3%, Time = 4 years
    • 3,500 * 0.043 * 4 = 602
    • Total to withdraw = 3,500 + 602 = 4,102
  • P = 20,000, I = 7.6%, Time = 10 years
    • 20,000 * 0.076 * 10 = 15,200
    • Total to withdraw = 20,000 + 15,200 = 35,200

Example: Andrew's Loan

• Andrew borrows $2,000 with an annual interest rate of 12.45%. He pays it back after 7 months. How much will Andrew pay the lender?
• Note: the interest rate is annual, but the time period is in months.
  • Option 1: divide annual interest rate by 12.
  • Option 2: convert time of 7 months into years (by dividing by 12.)
• 12. 45 / 12 = 1.0375.
• 0. 010375
• Principal is 2,000.
• I = PRT.
• 2000 * 0.010375 * 7 = 145.25.
• The Amount that needs to be paid back = 2,000 + 145.25 = 2145.25

Elizabeth's Tablet

• Elizabeth buys a $450 tablet on credit with 12.9% annual interest.
• In dollars, how much interest will she pay in a month?
  • 12. 9 % / 12 = 1.075%
  • 1. 075 = 0.01075.
  • .450 * 0.01075 * 1 = 4.8385 cents.
• In a Day?
  • P stays at 4.50
  • R = 0.129
  • T = 1 / 365
  • 450 * 0.129 * 1 = 58.05
  • 58. 05 / 365 = 0.159 cents

Credit Card Debts

• Credit card has monthly interest rate of 1.09%
• If you purchase a $690 couch with that card, but take 2 years to pay it back
• Principal = 690
• Interest rate = 1.09 = 0.0109
• Time = 2 years = 24 months.
• 70 * 0.0109 * 24 = 180.504

Comparing Two Loans

• Jerry takes 850 loan with 10.8% annual interest for ten months. How much less interest would he have paid if instead he had taken a loan with 9.5% annual interest, but this time for seven months?
• 8 * 850 *
• 0. 0108 * 0 = 76.5
• 0. 095 = 47.1041667
• 7 - 47.10 = = 29.40 less in interest

Financing a Car

• John uses his credit card to finance a car for $26,000 the annual interest is low, it is 2.75%, but only for the first 12 months. After that, if John hasn't paid the full amount back. The annual interest rate jumps to 9.95%

• Part 1 = Principal 26,000 * 0.0275 * Time of 1 = 715.

• Part 2 = Principal 26,000 * rate 9.95=0.0995 * 1.5 =3,880.5

• Total payback 3,880.5+ 715 +26,000 = 30,595.5$##. Eric's Borrowing