Financial Mathematics Problem: Calculating Accumulated Interest
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Questions and Answers

What is the formula used to calculate the accumulated interest?

  • S = P (1 + rt) (correct)
  • r = 1−dt
  • P = S(1−dt)
  • I = P rt

    • What is the value of the accumulated interest?

  • R1 530 (correct)
  • R1 700
  • R1 600
  • R1 500

    • What is the relationship between the simple interest rate and the simple discount rate?

  • r = 1+dt
  • r = 1/dt
  • r = 1−dt (correct)
  • r = dt

    • What is the formula used to calculate the simple interest?

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

    What is the purpose of rearranging the formula to have t as the subject?

    <p>To find the time period t, given the simple interest rate and simple discount rate</p> Signup and view all the answers

    What is the formula used to calculate the present value, given the future value and discount rate?

    <p>P = S(1−dt)</p> Signup and view all the answers

    What is the purpose of changing the answer to negative in financial mode?

    <p>To indicate a cash outflow</p> Signup and view all the answers

    What is the formula used in this problem to calculate the future value?

    <p>FV = PV × (1 + i)^n</p> Signup and view all the answers

    What is the value of 't' in the time line?

    <p>t = 365 + 24/365 + 9/12</p> Signup and view all the answers

    What is the purpose of dividing the days by 365?

    <p>To convert days to years</p> Signup and view all the answers

    What is the formula used to calculate the interest rate 'j'?

    <p>j = I/Y × 12</p> Signup and view all the answers

    What is the method used in this problem?

    <p>Fractional compounding</p> Signup and view all the answers

    What is the result of the calculation 385 579.29?

    <p>The future value</p> Signup and view all the answers

    What is the purpose of expressing the odd periods as a fraction of a year?

    <p>To express the time period in years</p> Signup and view all the answers

    What is the value of z in the given problem?

    <p>0.104 ÷ 2</p> Signup and view all the answers

    How do you calculate the number of half years until the maturity date if the month of the next coupon date is the same as the month of the maturity date?

    <p>Subtract the year of the next coupon date from the year of the maturity date</p> Signup and view all the answers

    What is the first step in calculating the number of half years until the maturity date?

    <p>Determine the first coupon date after the settlement date</p> Signup and view all the answers

    What is the HP10BII calculator used for in the problem?

    <p>To calculate the price of the Bond 525</p> Signup and view all the answers

    What is the value of d in the given problem?

    <p>9.6 ÷ 2</p> Signup and view all the answers

    What is the settlement date of the Bond 525?

    <p>17/05/14</p> Signup and view all the answers

    What is the number of half years from the coupon date after the settlement date, until the maturity date?

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

    What is the value of the first payment X moved forward from month two to month five?

    <p>X(1 + 0,16/12)3/12×12</p> Signup and view all the answers

    What is the value of the total payments at month five?

    <p>X(1 + 0,16/12)(3/12×12) + 2X + 3X(1 + 0,16/12)(5/12×12)</p> Signup and view all the answers

    What is the simplified expression of the total payments at month five?

    <p>X[(1 + 0,16/12)(3/12×12) + 2 + 3/(1 + 0,16/12)(5/12×12)]</p> Signup and view all the answers

    What is the value of X?

    <p>1 582,43</p> Signup and view all the answers

    What is the value of the payment at month five?

    <p>R3 164,86</p> Signup and view all the answers

    How many months is the first payment X moved forward?

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

    What is the value of 3X moved back from month ten to month five?

    <p>3X(1 + 0,16/12)(5/12×12)</p> Signup and view all the answers

    What is the key characteristic of a perpetuity?

    <p>The payments are made indefinitely.</p> Signup and view all the answers

    In a deferred annuity, when do you make the first payment?

    <p>A number of payment intervals after the end of the first interest period.</p> Signup and view all the answers

    What is the purpose of 'discounting back' in a deferred annuity?

    <p>To calculate the present value of the payments.</p> Signup and view all the answers

    What is the formula used to calculate the payment in an amortization?

    <p>P = R((1+i)^n - 1)/i</p> Signup and view all the answers

    What is the main difference between a deferred annuity and a perpetuity?

    <p>The timing of the first payment.</p> Signup and view all the answers

    What is the term used to describe the process of moving the present value of the payments back to the present?

    <p>Discounting back.</p> Signup and view all the answers

    Study Notes

    Simple Interest and Simple Discount

    • The formula for simple interest is: I = P rt
    • The formula for simple discount is: P = S (1 - dt)
    • The relationship between the simple interest rate and the simple discount rate is: r = 1 - dt

    Compound Interest

    • The formula for compound interest is: S = P (1 + rt)
    • The formula for ordinary compound interest is: S = P (1 + j/m)^(mt)
    • The formula for fractional compounding is: S = P (1 + j/m)^(mt) where t is a fraction of a year

    Time Lines and Periods

    • A time line is a graphical representation of the periods involved in a problem
    • Periods can be expressed as a fraction of a year
    • Days can be converted to years by dividing by 365

    Calculations using the HP10BII Calculator

    • Use normal mode for calculations
    • Use the formula: I = P rt to calculate the accumulated interest
    • Use the formula: S = P (1 + rt) to calculate the compound interest

    Odd Period Calculations

    • Use the method of fractional compounding to calculate the value of the total payments
    • Express the odd periods as a fraction of a year
    • Calculate the value of the payments at the specified month

    Bond Pricing

    • The formula for the all-in price of a bond is: P = danz + 100(1 + z)^(-n)
    • The number of half years (n) can be calculated using the following tips:
      • Determine the first coupon date after the settlement date
      • Determine the number of half years until the maturity date
      • Subtract the year of the next coupon date from the year of the maturity date to get the number of years until maturity

    Perpetuity

    • The formula for perpetuity is: P = R / i
    • You will receive the payment R indefinitely

    Deferred Annuity

    • With a deferred annuity, you are unable to start to repay your debt immediately
    • Your first payment is a number of payment intervals after the end of the first interest period
    • First calculate the present value of the payments made and then discount this amount back to now by using compound interest

    Amortisation

    • Use the present value formula for annuities to determine the payment
    • The formula for amortisation is: P = R [(1 + i)^(-n) - 1] / i

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    Description

    This quiz involves solving a problem related to financial mathematics, specifically calculating accumulated interest. It requires applying mathematical concepts to real-world financial scenarios.

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