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Health 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.
TipThe 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 BasicsWhen 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 FormulaThe 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 PeriodsIn 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 DueBecause 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. What is the formula in finding the value of an ordinary annuity identify each variable represents?The formula for determining the present value of an annuity is PV = dollar amount of an individual annuity payment multiplied by P = PMT * [1 – [ (1 / 1+r)^n] / r] where: P = Present value of your annuity stream. PMT = Dollar amount of each payment. r = Discount or interest rate.
How do you calculate present value of an ordinary annuity?You can use the following formula to calculate an annuity's present value:. PV of annuity = P * [1 - ((1 + r) ^(-n)) / r]. Where:. P = periodic payment.. r = periodic interest rate.. n = number of periods.. Present value of annuity = $100 * [1 - ((1 + .05) ^(-3)) / .05] = $272.32.. =PV(rate,nper,pmt). =PV(.05,3,-100). What is the formula of general ordinary annuity?As per the formula, the present value of an ordinary annuity is calculated by dividing the Periodic Payment by one minus one divided by one plus interest rate (1+r) raise to the power frequency in the period (in case of payments made at the end of period) or raise to the power frequency in the period minus one (in case ...
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