What is the formula in finding the present value of a deferred annuity identify each variable 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.

What Is an Ordinary Annuity?

An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. While the payments in an ordinary annuity can be made as frequently as every week, in practice they are generally made monthly, quarterly, semi-annually, or annually. The opposite of an ordinary annuity is an annuity due, in which payments are made at the beginning of each period. These two series of payments are not the same as the financial product known as an annuity, though they are related.

Key Takeaways

• An ordinary annuity is a series of regular payments made at the end of each period, such as monthly or quarterly.
• In an annuity due, by contrast, payments are made at the beginning of each period.
• Consistent quarterly stock dividends are one example of an ordinary annuity; monthly rent is an example of an annuity due.

What's an Ordinary Annuity?

How an Ordinary Annuity Works

Examples of ordinary annuities are interest payments from bonds, which are generally made semiannually, and quarterly dividends from a stock that has maintained stable payout levels for years. The present value of an ordinary annuity is largely dependent on the prevailing interest rate.

Because of the time value of money, rising interest rates reduce the present value of an ordinary annuity, while declining interest rates increase its present value. This is because the value of the annuity is based on the return your money could earn elsewhere. If you can get a higher interest rate somewhere else, the value of the annuity in question goes down.

Present Value of an Ordinary Annuity Example

The present value formula for an ordinary annuity takes into account three variables. They are as follows:

• PMT = the period cash payment
• r = the interest rate per period
• n = the total number of periods

Given these variables, the present value of an ordinary annuity is:

• Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)

For example, if an ordinary annuity pays $50,000 per year for five years and the interest rate is 7%, the present value would be:

• Present Value = $50,000 x ((1 - (1 + 0.07) ^ -5) / 0.07) = $205,010

An ordinary annuity will have a lower present value than an annuity due, all else being equal.

Present Value of an Annuity Due Example

Recall that with an ordinary annuity, the investor receives the payment at the end of the time period. That stands in contrast to an annuity due, in which the investor receives the payment at the beginning of the period. A common example is rent, where the renter typically pays the landlord in advance for the month ahead. This difference in payment timing affects the value of the annuity. The formula for an annuity due is as follows:

• Present Value of Annuity Due = PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)

If the annuity in the above example was instead an annuity due, its present value would be calculated as:

• Present Value of Annuity Due = $50,000 + $50,000 x ((1 - (1 + 0.07) ^ -(5-1) / 0.07) = $219,360.

All else being equal, an annuity due is always worth more than an ordinary annuity, because the money is received earlier.

What is the formula in finding the present value of a deferred annuity identify each variables represent?

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

What is deferred annuity formula?

What's the present value of a 4 year ordinary annuity of $2 250?