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

Annuities are investment contracts issued by financial institutions like insurance companies and banks. When you purchase an annuity, you invest your money in a lump sum or gradually during an “accumulation period.” At a specified time the issuer must start making regular cash payments to you for a specified period of time. The future value of an annuity is an analytical tool an annuity issuer uses to estimate the total cost of making the required cash payments to you.

Tip

The formula for the future value of an ordinary annuity is F = P * ([1 + I]^N - 1 )/I, where P is the payment amount. I is equal to the interest (discount) rate. N is the number of payments (the “^” means N is an exponent). F is the future value of the annuity.

Annuity Basics

When you purchase an annuity, the issuer invests your money to produce income. The agreement is a contract that transfers the risk from the individual to the insurance company, or annuity issuer, says U.S. News. Annuity issuers make their money by keeping a part of the investment income, which is referred to as the discount rate.

However, as each payment is made to you, the income the annuity issuer makes decreases. For the issuer, the total cost of making the annuity payments is the sum of the cash payments made to you plus the total reduction of income the issuer incurs as the payments are made. Issuers calculate the future value of annuities to help them decide how to schedule payments and how large their share (the discount rate) must be to cover expenses and make a profit.

Future Value of Annuity Formula

The formula for the future value of an annuity varies slightly depending on the type of annuity. Ordinary annuities are paid at the end of each time period. Annuities paid at the start of each period are called annuities due. Many annuities are paid yearly. However, some annuities make payments on a semiannual, quarterly or monthly schedule.

The basic equation for the future value of an annuity is for an ordinary annuity paid once each year. According to Trusted Choice, the ordinary annuity formula is F = P * ([1 + I]^N - 1 )/I. P is the payment amount. I is equal to the interest (discount) rate. N is the number of payments (the “^” means N is an exponent). F is the future value of the annuity. For example, if the annuity pays $500 annually for 10 years and the discount rate is 6 percent, you have $500 * ([1 + 0.06]^10 - 1 )/0.06. The future value works out to $6,590.40. This means that, at the end of 10 years, the issuer’s total cost is equal to $6,590.40 ($5,000 in payments plus $1,590.40 in interest not earned).

Payment Periods

In order to use the equation for future value of an annuity when the payment interval is less than one year, you must make two adjustments. First, divide the discount rate (I) by the number of payments per year to find the rate of interest paid each month. Use this monthly rate as your value for I. Second, multiply the number of annual payments (N) by the number of payments each year to find the total number of payments and use this value for N.

Annuity Due

Because payments for an annuity due are made at the beginning of the payment period, the future value of the annuity is increased by the interest earned for one time period. Start by calculating the future value using the equation for an ordinary annuity for the appropriate time period. Then multiply the result by 1 + I where I is equal to the discount rate for the period.

Identify each variable represents.4.What is the formula in finding the present value of an ordinary annuity?Identify each variable represents.5.What is the periodic payment formula of an annuity?

What’s more..Answer as indicated. Write your answers in a separate sheet of paper.1.Find the future value of an ordinary annuity with a regular payment ofP1,000 at 5% compounded quarterly for 3 years.2.Find the present value of an ordinary annuity with regular quarterlyopayments worth P1,000 at 3% annual interest rate compoundedquarterly at the end of 4 years.What have I have learned..Complete the sentence below. Write your answers on a separate sheet of paper.1._____________________________________ is a sequence of payments made atequal (fixed) intervals or periods of time.2._____________________________________ is the sum of present value of allthe payments to be made during the entire term of the annuity.3._____________________________________ is an annuity where the paymentinterval is the same as the interest period.4._____________________________________ is a type of annuity in which thepayments are made at the end of each payment interval.5._____________________________________ is the sum of future values of allpayments to be made during the entire term of the annuity.

What I can do…Solve for the following problems. Answer as indicated. Write your answers in aseparate sheet of paper.1.Mr. Ribaya paid P200,000 as downpayment for a car. The remainingamount is to be settled by paying P16,200 at the end of each month for 5years. If interest is 10.5% compounded monthly, what is the cash price ofhis car?2.In order to save for her high school graduation, Marie decided to saveP200 at the end of each month. If the bank pays 0.250% compoundedmonthly, how much will her money be at the end of 6 years?3.Paolo borrowed P100,000. He agrees to pay the principal plus interest bypaying an equal amount of money each year for 3 years. What should behis annual payment if interest is 8% compounded annually?

Additional Activities…Answer as indicated. Write your answers in a separate sheet of paper.1.In a certain account providing an interest rate of r compounded quarterly,P2,500 is deposited every end of the quarter. What value of r will make thefuture value of the account P5,200 in six months?

General AnnuityLesson2What I need to know…At the end of the lesson, the learner will be able to:✓Illustrate general annuities✓Find the future and present values of general annuitiesand compute the periodic payment of a general annuity✓Calculate the fair market value of a cash flow streamthat includes an annuity.What’s in…REVIEWIn the previous lessons, you learned to illustrate a Simple Annuity and yousolve the present and future values of simple Annuity. You also compute for theperiodic payment of simple annuity. As well as solve problems involving real lifesituations on simple Annuities.What’s new…Examples of General annuity:1.Monthly installment payment of a car, lo or house with an interest ratethat is compounded annually.

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

How do you calculate present value of an ordinary annuity?