Compound Interest Calculation Quiz
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Questions and Answers

What is the total amount in Esther's account at the end of four years?

  • ₱8,000
  • ₱8,161.51 (correct)
  • ₱8,350
  • ₱8,500

    • What is the formula used to calculate the compound amount A?

  • A = P(1 + r)^n
  • A = P(1 + r/n)^(nt) (correct)
  • A = P + Prt
  • A = P + I

    • How much interest does Esther earn on her investment?

  • ₱150
  • ₱180
  • ₱161.51 (correct)
  • ₱200

    • What is the present value (P) in the example for the 20-year investment?

    <p>₱20,000</p> Signup and view all the answers

    What is the principal amount in Esther's investment?

    <p>₱8,000</p> Signup and view all the answers

    What does the future value represent in an investment?

    <p>The total value at a given interest rate</p> Signup and view all the answers

    If the interest rate is 0.5%, what is the corresponding decimal representation of this rate?

    <p>0.005</p> Signup and view all the answers

    How many total compounding periods are there in Esther's investment?

    <p>16</p> Signup and view all the answers

    How much total amount will be available after 20 years of investment of ₱20,000 at 4% interest compounded monthly?

    <p>₱44,451.64</p> Signup and view all the answers

    What is the maturity value of an investment?

    <p>The amount it is worth in the future</p> Signup and view all the answers

    Which of the following correctly represents the formula for calculating the compound amount?

    <p>A = P(1 + rac{r}{m})^{mn}</p> Signup and view all the answers

    What does the symbol 'I_C' represent in the context of compound interest?

    <p>The compound interest earned</p> Signup and view all the answers

    What variables are used to calculate compound interest?

    <p>Principal, time, and compounding frequency</p> Signup and view all the answers

    Which of the following is NOT a common value for the number of compounding periods in a year?

    <p>10 for decennially</p> Signup and view all the answers

    What is the total amount in Esther's account after four years with quarterly compounding?

    <p>₱8,323.12</p> Signup and view all the answers

    What is the definition of compound interest?

    <p>Interest added to the principal for future calculations</p> Signup and view all the answers

    What is the formula for calculating simple interest?

    <p>𝐼 = 𝑃𝑟𝑡</p> Signup and view all the answers

    If you invested ₱15,000 at a simple interest rate of 5% for 4 years, what is the interest earned?

    <p>₱6,000</p> Signup and view all the answers

    What value of 't' in the interest formula represents if the period is expressed in years?

    <p>The fraction of a year invested</p> Signup and view all the answers

    What does the future value formula indicate about the relationship between investment amount and interest rate?

    <p>Higher interest rates increase future value.</p> Signup and view all the answers

    In the context of finance, what does the variable 𝐹 represent?

    <p>The future value of an investment.</p> Signup and view all the answers

    If the principal amount is ₱20,000 and the total interest earned in 2 years is ₱1,200, what is the interest rate?

    <p>3%</p> Signup and view all the answers

    What is the purpose of the formula for present value?

    <p>To determine the amount to invest today for a future target.</p> Signup and view all the answers

    What is the formula to calculate maturity value (MMM)?

    <p>MMM = P(1 + r)</p> Signup and view all the answers

    How would you express 9 months in years for interest calculations?

    <p>0.75 years</p> Signup and view all the answers

    If you want to accumulate ₱2,000,000 in 45 years at a 3% interest rate compounded quarterly, what is the calculated present value?

    <p>₱521,098.87</p> Signup and view all the answers

    If the principal (P) is ₱40,000 and the interest (I) is ₱9,600, what is the maturity value (MMM)?

    <p>₱49,600</p> Signup and view all the answers

    If a total simple interest of ₱4,500 is earned over a period of 3 years, with a principal of ₱15,000, what is the rate of interest?

    <p>7.5%</p> Signup and view all the answers

    Given a principal of ₱32,000, an interest rate of 8%, and a time period of 180 days, what is the maturity value (MMM)?

    <p>₱33,280</p> Signup and view all the answers

    What does the variable 𝑚 represent in the formulas provided?

    <p>The total number of compounding periods per year.</p> Signup and view all the answers

    In the context of simple interest, what does 'P' represent?

    <p>The principal amount invested</p> Signup and view all the answers

    If you borrow ₱25,000 and pay ₱2,500 in interest over 1 year, what is the effective rate of interest?

    <p>10%</p> Signup and view all the answers

    How do you calculate the interest (I) using the principal (P) and the rate (r)?

    <p>I = Prt</p> Signup and view all the answers

    What would be the future value of ₱15,000 compounded semi-annually for five years at 6% interest?

    <p>₱20,158.75</p> Signup and view all the answers

    When calculating present value, what does the term 𝑛 represent?

    <p>The total number of compounding periods over the investment duration.</p> Signup and view all the answers

    What is the value of I when the principal is ₱37,500, the rate is 8%, and the time is 146 days?

    <p>₱1,200</p> Signup and view all the answers

    What does the term 'maturity value' refer to in finance?

    <p>The total amount owed after interest is added</p> Signup and view all the answers

    What happens to the present value if the interest rate increases while keeping the future value constant?

    <p>The present value decreases.</p> Signup and view all the answers

    Which statement correctly describes the relationship between interest and principal?

    <p>Interest is derived from the principal multiplied by the rate and time.</p> Signup and view all the answers

    What is the correct value of the principal (P) if the interest earned (Ie) is ₱1,200 at an 8% rate for 146 days?

    <p>₱37,500</p> Signup and view all the answers

    How much must be invested today to reach ₱2,000,000 in 45 years?

    <p>₱521,098.87</p> Signup and view all the answers

    If the interest rate (r) is unknown, which formula should be used?

    <p>$r = m imes (F/P - 1)$</p> Signup and view all the answers

    When the number of compounding periods (m) is unknown, which expression is used?

    <p>$m = rac{n}{F/P}$</p> Signup and view all the answers

    What is the formula to find the total number of compounding periods (n) when unknown?

    <p>$n = rac{F}{P imes r}$</p> Signup and view all the answers

    When time is unknown, how can total compounding periods (n) be expressed?

    <p>$t = rac{n}{m}$</p> Signup and view all the answers

    What does the variable F represent in future value calculations?

    <p>Future value amount</p> Signup and view all the answers

    In the context of compounding, which of the following factors is NOT a variable needed to calculate future value?

    <p>Market volatility (v)</p> Signup and view all the answers

    If you want to calculate future value, which of the following formulas must NOT include the logarithm?

    <p>$F = P(1 + r)^n$</p> Signup and view all the answers

    Study Notes

    Simple Interest

    • Simple interest is a fixed percentage of the total invested amount paid yearly.
    • Formula: I = Prt, where:
      • I = Simple interest
      • P = Principal (amount invested)
      • r = Interest rate (percentage)
      • t = Time (number of years)
    • Formulas for unknown variables:
      • P = I / rt
      • r = I / Pt
      • t = I / Pr

    Example 1

    • Suppose P10,000 is deposited with a 10% simple interest rate for 3 years.
    • Calculate the interest earned: I = P10,000 * 0.10 * 3 = P3,000

    Example 2

    • Cyndi borrowed P30,000.
    • The interest paid was P3,375 over 9 months.
    • Calculate the interest rate: r = 0.15 (using appropriate formula) or 15%.

    Ordinary Interest

    • Ordinary interest calculates simple interest based on a 360-day year.

    Example 3

    • Miss Uy borrowed P80,000.
    • The loan earned P5,400 at 9% ordinary interest.
    • Calculate the number of days it took to repay: t= 270 days

    Exact Interest

    • Exact interest calculates simple interest based on a 365-day year.

    Example 4

    • Mr. Sandoval paid P1,200 exact interest at 8% for 146 days.
    • Calculate the principal: P = P37,500

    Compound Interest

    • Interest due is added to the previous balance, becoming the new principal for the next period.
    • Compound interest (Ic): Interest added to the principal.
    • Compound amount (A): Total amount at the end of the last period.
    • Formula: A = P(1 + r/m)^ (mn) where:
      • P = Principal (present value)
      • r = Annual interest rate
      • m = Number of compounding periods per year
      • n= Total number of compounding periods

    Example 5

    • Esther deposited P8,000 in a savings account.
    • Compounded quarterly at 0.5% for four (4) years.
    • Compound amount: A = P8,161.51
    • Compound interest: Ic= P161.51

    Example 6

    • How much interest is earned after 20 years by P20,000 at 4% interest compounded monthly.
    • Compound amount: A = P44,451.64
    • Compound interest: Ic= P24,451.64

    Maturity Value

    • The final amount of an investment or debt with added interest.
    • Formula: MV = P(1+rt)

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    Test your understanding of compound interest with this quiz. Answer questions regarding formulas, principal amounts, interest rates, and investment growth over time. Perfect for finance enthusiasts or anyone looking to sharpen their investment knowledge.

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