Future Value and Present Worth Concepts
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Questions and Answers

If the interest rate is 10%, what amount should be deposited now to provide for three end-of-year withdrawals of P10000?

  • P24,868.52 (correct)
  • P30,000.00
  • P18,500.00
  • P20,000.00

    • What is the formula for calculating the present worth (P) based on a uniform series (A)?

  • P = A * (P/A, i%, n) (correct)
  • P = A / (1+i)^n
  • P = A + (P/A, i%, n)
  • P = A * (1+i)^n

    • What is the value of F1 after the first end-of-year adjustment when P10000 is withdrawn?

  • P27,355.37
  • P24,868.52
  • P17,355.37 (correct)
  • P9,090.91

    • For a car bought with a 50% down payment and monthly payments of P8,000 over 5 years at an interest rate of 7%, what is the present value of the car?

    <p>P360,000.00</p> Signup and view all the answers

    In the scenario of a fund for end-of-year withdrawals, which aspect is critical for determining the initial deposit amount?

    <p>The interest rate applied over the periods</p> Signup and view all the answers

    What does future value (FV) estimate?

    <p>The value of a current asset at a future date based on an assumed rate of growth</p> Signup and view all the answers

    What impact does inflation have on the future value of an asset?

    <p>It can negatively affect the future value by eroding its worth</p> Signup and view all the answers

    What does Present Worth (PV) represent?

    <p>The value of future cash flows at a given discount rate</p> Signup and view all the answers

    How does a higher discount rate affect present value?

    <p>It decreases the present value of future cash flows</p> Signup and view all the answers

    What is indicated by the notation 'P' in financial calculations?

    <p>The present sum of money at a reference point in time</p> Signup and view all the answers

    Which formula is used to find present worth 'P' given future worth 'F'?

    <p>P = F [P/F, i%, n]</p> Signup and view all the answers

    What does the symbol 'n' represent in financial formulas?

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

    If a firm wants to have Php 1,000 six years from now, what is being calculated?

    <p>The present value to invest today to reach that future amount</p> Signup and view all the answers

    What is the effective annual interest rate equivalent to 12% compounded quarterly?

    <p>11.88%</p> Signup and view all the answers

    If you deposit Php 600 at the end of every month for 4 years at an interest rate of 12% compounded quarterly, what will be the future worth?

    <p>Php 64,641.32</p> Signup and view all the answers

    What formula is used to calculate the future value when the interest rate and cash flow period is given?

    <p>F = A(1 + i)^n</p> Signup and view all the answers

    How is the nominal interest rate commonly compared in different compounding periods?

    <p>Using effective annual rate calculations.</p> Signup and view all the answers

    What is the purpose of bringing a salvage value to its present value when calculating the capital recovery of a tool?

    <p>To ensure it does not interfere with computations.</p> Signup and view all the answers

    What is the value of cash flow that generates a future worth of Php 64,641.32 if invested at 11.88% compounded monthly for 4 years?

    <p>Php 600</p> Signup and view all the answers

    Which of these accurately describes the cash flows in the future value calculations?

    <p>They can vary in amount and frequency.</p> Signup and view all the answers

    What is the capital recovery of a workshop tool that costs P18,000 with a salvage value of P3,000 over 10 years at a rate of 15%?

    <p>P2,520</p> Signup and view all the answers

    What is the monthly interest rate if the annual nominal rate is 7%?

    <p>0.005833</p> Signup and view all the answers

    How many total compounding periods are there in 5 years when compounded monthly?

    <p>60</p> Signup and view all the answers

    What is the annual amount to deposit to accumulate Php 10,000 at the time of the third deposit at an interest rate of 10%?

    <p>Php 3,021.15</p> Signup and view all the answers

    If you want to have $500,000 in your retirement account after 25 years at an 8% annual interest rate, how much should you deposit at the end of each quarter?

    <p>$1,601.37</p> Signup and view all the answers

    What is the formula for calculating the annual payment A required to repay a loan of P when the interest rate is i and there are n payments?

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

    To accumulate P 404,015.948 after 60 periods at a monthly interest rate of 0.005833, what is A when calculated with the corresponding formula?

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

    What does the factor functional symbol (A/F, i%, n) represent in financial calculations?

    <p>Future value of a uniform series</p> Signup and view all the answers

    If the first payment of a loan is due one year after receiving the loan, and the loan is for Php 1,000, what must be determined to know the size of the payments?

    <p>The interest rate and number of payments</p> Signup and view all the answers

    What is the monthly installment amount for a car costing 450,000 with a 50,000 down payment and a 12% effective interest rate over 24 months?

    <p>₱18,715.00</p> Signup and view all the answers

    How is the interest rate per month calculated from an effective annual interest rate of 12%?

    <p>0.00949</p> Signup and view all the answers

    What formula is used to calculate the number of periods (n) when given future worth (F) and present worth (P)?

    <p>n = ln(F) / ln(1 + i)</p> Signup and view all the answers

    What does the term 'effective interest rate' signify when calculating payments?

    <p>The actual rate considering compounding</p> Signup and view all the answers

    To find the nominal rate using the effective interest rate of 12% compounded quarterly, what is the first step?

    <p>Divide the effective rate by 4.</p> Signup and view all the answers

    What is the effective annual interest rate for a nominal rate of 12% compounded quarterly?

    <p>0.125509</p> Signup and view all the answers

    What is the present worth (P) if the future worth (F) is 600 at an interest rate (i) of 0.12 over n periods?

    <p>P = 600 / (1 + 0.12)^n</p> Signup and view all the answers

    What is the total amount saved after depositing P600 every month for 4 years at an interest rate of 12% compounded quarterly?

    <p>₱28,800</p> Signup and view all the answers

    What is the future value of Alan's deposit of $300 at the end of 6 years at a 10% monthly compounded interest?

    <p>$29,663</p> Signup and view all the answers

    In a deferred annuity, when are the first payments typically made?

    <p>After a certain number of compounding periods</p> Signup and view all the answers

    How much will the contributions in the first retirement plan be worth after 35 years if it earns 8% interest annually?

    <p>$43,698</p> Signup and view all the answers

    What is the formula used to compute the future value of an annuity when making periodic payments?

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

    How is the future value calculated for the deferred annuity after stopping the contributions?

    <p>Bringing the annuity value to the last year before the compounding ends</p> Signup and view all the answers

    If a deferred annuity is set to make 10 payments starting a year after the first deposit, how many total compounding periods must be accounted for?

    <p>11</p> Signup and view all the answers

    What characterizes a deferred annuity in contrast to an ordinary annuity?

    <p>Payments start after a delay</p> Signup and view all the answers

    What is a crucial step when calculating the future value of a deferred annuity?

    <p>Using the value at the end of the last payment as present value for the period after</p> Signup and view all the answers

    Study Notes

    Future Value and Present Worth

    • Future value (FV) is the value of a current asset at a future date, based on an assumed rate of growth.
    • Future value is used to estimate how much an investment made today will be worth in the future.
    • Factors such as inflation can negatively impact future value by reducing asset value.
    • Present worth (PV) is the sum of money that, if invested now at a given rate of compound interest, will accumulate to a specified amount at a specified future date.
    • Future cash flows are discounted at the discount rate. The higher the discount rate, the lower the present value of the future cash flows.

    Symbolic Notations

    • i = effective interest rate per interest period
    • n = number of compounding (interest) periods
    • P = present sum of money; equivalent value of one or more cash flows at a reference point in time (present)
    • F = future sum of money; equivalent value of one or more cash flows at a reference point in time (future)
    • A = end-of-period cash flows (or equivalent end-of-period values) in a uniform series

    Compound Interest

    • Interest is calculated on the accumulated interest charges up to the beginning of each interest period.
    • Formula: Fn = P(1 + i)^n
      • Fn = total amount accumulated or owed after n interest periods
      • P = principal amount

    Relating Present and Future Values of Single Cash Flows

    • Formula: P = F [ 1 / (1 + i)^n]
    • (P/F, i%, n) is the factor functional symbol

    Finding P given F

    • Single payment, present worth factor
    • Factor functional symbol (P/F, i%, n)
    • Formula: P = F (P/F, i%, n)
    • P = present worth
    • F = future value
    • i = interest rate
    • n = number of periods

    Relating a Uniform Series (Annuity) to its Present and Future Equivalent Values

    • Annuity: a series of payments made at equal intervals.
    • Four general problems in solving annuity:
      • Finding F given A
      • Finding P given A
      • Finding A given F
      • Finding A given P

    Finding F given A

    • Uniform series, compound amount factor.
    • Factor functional symbol (F/A, i%, n).
    • Formula: F = A [ (1 + i)^n - 1 / i].

    Finding P given A

    • Uniform series, present worth factor.
    • Factor functional symbol (P/A, i%, n).
    • Formula: P = A [ (1 + i)^n - 1 / i(1 + i)^n]

    Finding A given F

    • Uniform series, sinking fund factor.
    • Factor functional symbol (A/F, i%, n).
    • Formula: A = F [ i / (1 + i)^n - 1]

    Finding A given P

    • Uniform series, capital recovery factor.
    • Factor functional symbol (A/P, i%, n)
    • Formula: A = P [ i(1 + i)^n / (1 + i)^n -1 ]

    Annuity Due

    • In annuity due, the equal payments are made at the beginning of each compounding period.
    • Formula for future value (F) Given (A) : F = A [(1+ i)^n – 1]/ i * (1+ i)
    • Formula for present value (P) Given (A): P = A [1 – (1 + i)^(-n)]/ i * (1 + i)

    Deferred Annuity

    • In deferred annuity, the first payment is a certain number of compounding periods after the first.
    • Cash flows in a deferred annuity form an ordinary annuity.

    Perpetuity

    • Perpetuity is an annuity where the payment period extends forever, meaning the periodic payments continue indefinitely.

    • Formula for present value (P) of perpetuity: P = A / i

    • The future value is not defined in perpetuity.

    Other Important Notes

    • Understand the equivalence of values and how time affects them.
    • Store as many decimal places as possible in your calculations.

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    ENSC 31 Future Value and Present Worth PDF

    Description

    Test your understanding of future value and present worth concepts in finance. This quiz covers the definitions, formulas, and factors affecting the future value of investments. Learn how to apply these concepts to determine the worth of investments over time.

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