Compound Interest Basics
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Questions and Answers

What is the primary purpose of compound interest?

  • To maintain the principal amount
  • To provide a fixed payment over time
  • To increase the principal amount periodically (correct)
  • To decrease the principal amount periodically

    • Compound interest is calculated only once at the end of the investment period.

    False

    How long must Php10,000 be invested at a rate of 5% compounded monthly to reach Php10,511.62?

    1 year

    The formula for calculating the time in years for compound interest is __________.

    <p>t = n [ log(F ÷ P) ÷ log(1 + (r/n)) ]</p> Signup and view all the answers

    If a man invests Php 5,000 at 6% interest compounded quarterly, what will be the compounding periods in 3 years?

    <p>24</p> Signup and view all the answers

    What rate must be earned for an investment of Php 250,000 to yield Php 10,500 in 4 years and 9 months, compounded monthly?

    <p>2.04%</p> Signup and view all the answers

    Match the following types of interest compounding with their corresponding frequency:

    <p>Semi-Annually = Every 6 months Quarterly = Every 3 months Monthly = Every 1 month Annually = Every 12 months</p> Signup and view all the answers

    The compound amount after investing ₱7,500 at 3% compounded monthly for 3 years and 3 months will be __________.

    <p>₱8,122.37</p> Signup and view all the answers

    What defines an annuity due?

    <p>Payments are made at the beginning of each payment interval.</p> Signup and view all the answers

    A simple annuity has the same payment interval as the interest period.

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

    Which type of annuity involves payments that extend over an indefinite length of time?

    <p>Contingent annuity</p> Signup and view all the answers

    Payments made at the end of each period characterize an __________ annuity.

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

    What is the primary characteristic of a general annuity?

    <p>Payment intervals are not the same as the interest periods.</p> Signup and view all the answers

    Match the following situations with the type of annuity:

    <p>Monthly rent payments are made at the beginning of each month = Annuity Due Company pays retirement contributions at the end of each period = Ordinary Annuity Depositing money at the beginning of every quarter = Annuity Due Insurance premiums paid at the start of each year = Annuity Due</p> Signup and view all the answers

    Provide an example of a situation where a payer makes payments by installment.

    <p>Paying for a car loan monthly.</p> Signup and view all the answers

    If a person saves $100 at the beginning of each month for a year at 5% compounded monthly, this scenario is best described as:

    <p>Annuity Due</p> Signup and view all the answers

    Which formula represents the future value of an ordinary annuity?

    <p>$FV_{OA} = A \frac{(1+i)^n - 1}{i}$</p> Signup and view all the answers

    An annuity due has payments made at the beginning of each period.

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

    What does 'A' stand for in annuity formulas?

    <p>Equal payments</p> Signup and view all the answers

    In a future value formula for a general annuity, the periodic interest rate is represented by __________.

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

    Match the following types of annuities with their characteristics:

    <p>Ordinary Annuity = Payments at the end of each period Annuity Due = Payments at the beginning of each period Simple Annuity = Fixed payments over a defined period General Annuity = Payments can vary over time</p> Signup and view all the answers

    Which of the following is a key characteristic of a simple annuity?

    <p>The payments are equal and fixed.</p> Signup and view all the answers

    The present value of an annuity cannot be calculated if the interest rate is zero.

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

    What is the significance of the variable 'n' in annuity formulas?

    <p>Number of compounding periods</p> Signup and view all the answers

    The formula for the future value of an annuity due is represented as __________.

    <p>$FV_{AD} = A \frac{(1+i)^n - 1}{i} (1+i)$</p> Signup and view all the answers

    Which term refers to the value of a series of future cash payments discounted back to the present?

    <p>Present Value</p> Signup and view all the answers

    What is the future value formula for an ordinary annuity?

    <p>$FV_{OA} = A rac{(1+i)^{n}-1}{i}$</p> Signup and view all the answers

    An annuity due pays at the end of each period.

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

    What is the key difference in payment timing between ordinary annuity and annuity due?

    <p>Ordinary annuity pays at the end of each period, while annuity due pays at the beginning.</p> Signup and view all the answers

    The future value of a series of payments made at the end of each quarter for 4 years at an interest rate of 4.8% compounded quarterly can be calculated using the formula __________.

    <p>$FV_{OA} = A \frac{(1+i)^{n}-1}{i}$</p> Signup and view all the answers

    Match the following annuities with their payment timing:

    <p>Ordinary Annuity = Payments at the end of each period Annuity Due = Payments at the beginning of each period General Annuity = Payments could be at any point in time Simple Annuity = Payments at regular intervals</p> Signup and view all the answers

    What would be the present value of a series of payments made at the beginning of each month for 2 years at an interest rate of 2% compounded monthly?

    <p>$PV_{AD} = A \frac{1-(1+i)^{-n}}{i}(1+i)$</p> Signup and view all the answers

    The present value of an annuity is always less than the future value of the same annuity.

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

    What is the periodic rate if the annual interest rate is 4.8% compounded quarterly?

    <p>1.2%</p> Signup and view all the answers

    The number of compounding periods for a payment made quarterly for 4 years is __________.

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

    The formula for calculating the future value of a general annuity due is given by:

    <p>$FV_{GAD} = A \frac{(1+i)^{n}-1}{p}(1+i)$</p> Signup and view all the answers

    Study Notes

    Compound Interest

    • Compound interest is the interest calculated on the principal amount and also on the accumulated interest of previous periods.
    • This increases the original amount borrowed or loaned over time until the transaction concludes.
    • The final amount (Compound Amount) is the sum of the principal and the accumulated interest.

    Compound Interest Formula

    • The formula for compound interest is: A = P(1 + r/n)^(nt)
      • A = the future value of the investment/loan, including interest
      • P = the principal investment amount (the initial deposit or loan amount)
      • r = the annual interest rate (decimal)
      • n = the number of times that interest is compounded per year
      • t = the number of years the money is invested or borrowed for

    Compounding Periods

    • The frequency of interest compounding affects the total interest earned.
    • Common compounding periods include annually, semi-annually, quarterly, and monthly.
    • The value of 'n' in the formula represents the number of times interest is compounded per time unit (often a year).

    Compounding Period Examples

    Compounding PeriodYearly Frequency (n)Annually1Semi-Annually2Quarterly4Monthly12

    Problem Solving Examples

    • Examples of compound interest problems are presented.
    • These illustrate how to find the final amount after a given period, with varying compounding frequencies.
    • A case study is given with sample data to explore compound interest concepts.
    • Specific examples include compounded semi-annually and compounded quarterly

    Other Formula

    • The formula t=log(F/P)nlog(1+r/n)t = \frac{log(F/P)}{n log(1 + r/n)}t=nlog(1+r/n)log(F/P)​ can calculate time (t) given the future value (F), Principal (P), interest rate (r), and compounding periods (n).
    • The formula r=n(FPnt−1)r = n(\sqrt[nt]{\frac{F}{P}} - 1)r=n(ntPF​​−1) calculates the rate of interest (r) given the future value (F), Principal (P), compounding periods (n), and time (t).

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    Description

    This quiz covers the fundamentals of compound interest, including its definition, formula, and the effects of different compounding periods. Test your understanding of how compound interest works and its impact on investments and loans.

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