What is the formula in finding the present value of an ordinary annuity identify each variable represent Brainly?

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mtor

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt   = 20,000(1 + 0.085/12)(12)(4)   = $28,065.30

Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.

Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1 + rnom /m)m   =   (1 + 0.098/12)12 - 1   =  0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P � r / [1 - (1 + r)-n]

D = P � (1 + r)k - R � [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x � P � r)] / log (1 + r)

Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i where i = r/m is the interest paid each period and n = m � t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =
5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12) = $23,763.28

Value of a Bond:

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the "what-if" scenarios by entering different numerical value(s), to make your "good" strategic decision.

Replace the existing numerical example, with your own case-information, and then click one the Calculate.

Test your knowledge of annuities.

Click the box below each question to see the correct answer. Keep track of how many you answer correctly and compare the total to the grading scale found at the bottom of the page.

Page One | Page Two |  Page Three

    0        1        2        3        4        5        6  Time line
    |--------|--------|--------|--------|--------|--------|
            $10      $10      $10      $10      $10          Cash flows
             ¦                                   ¦
             A                                   B
The present value of the 5-period annuity shown above as of Point A is the present value of a 5-period ______________ , whereas the future value of the same annuity as of Point B is the future value of a 5-period ______________ .
        A.  ordinary annuity; ordinary annuity.
        B.  ordinary annuity; annuity due.
        C.  annuity due; annuity due.
        D.  annuity due; ordinary annuity.
  10.Study the time line and accompanying 5-period cash-flow pattern below.

    0        1        2        3        4        5        6  Time line
    |--------|--------|--------|--------|--------|--------|
   $10      $10      $10      $10      $10       ¦           Cash flows
    ¦                                            ¦
    A                                            B
The present value of the 5-period annuity shown above as of Point A is the present value of a 5-period ______________ , whereas the future value of the same annuity as of Point B is the future value of a 5-period ______________ .
        A.  ordinary annuity; ordinary annuity.
        B.  ordinary annuity; annuity due.
        C.  annuity due; annuity due.
        D.  annuity due; ordinary annuity.
 

How did you do?

• All 10 correct = You are an annuity GURU!  Congratulations!
• 8 or 9 correct = Approaching zero defects -- just review what you missed.
• 6 or 7 correct = You need a little more work. Review page 2; then take the quiz again.
• 5 or fewer correct = You have some work to do: (a) review page 2; (b) try your hand at the practice time-value-of-money annuity problems (with answers and detailed solutions) found at: http://web.utk.edu/~jwachowi/annuity_prob.pdf ; and (c) then take the quiz again.

What is the formula in finding the present value of an ordinary annuity identify each variable represent?

How do you find the present value of an ordinary annuity?

What is ordinary annuity formula?