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The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities .
These expected future cash outflows are then discounted to reflect interest to the date of the expected cash flow. For example, if we expect to pay $300,000 in Year 1, $200,000 in year 2 and $150,000 in Year 3, and we are able to invest reserves to earn 8%p.a., the respective contributions to Actuarial Reserves are:
Equivalently C is the periodic loan repayment for a loan of PV extending over n periods at interest rate, i. The formula is valid (for positive n, i) for ni≤3. For completeness, for ni≥3 the approximation is . The formula can, under some circumstances, reduce the calculation to one of mental arithmetic alone.
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a halo system , where symbols are placed as superscript or subscript before or after the main letter.
The accounting rate of return, also known as average rate of return, or ARR, is a financial ratio used in capital budgeting. [27] The ratio does not take into account the concept of time value of money. ARR calculates the return, generated from net income of the proposed capital investment. The ARR is a percentage return.
Actuaries do not always attempt to predict aggregate future events. Often, their work may relate to determining the cost of financial liabilities that have already occurred, called retrospective reinsurance, [25] or the development or re-pricing of new products. [26] Actuaries also design and maintain products and systems.
Converting an annual interest rate (that is to say, annual percentage yield or APY) to the monthly rate is not as simple as dividing by 12; see the formula and discussion in APR. However, if the rate is stated in terms of "APR" and not "annual interest rate", then dividing by 12 is an appropriate means of determining the monthly interest rate.
The formula for SEC 30-day yield is = [(+)]. Where: a = dividends and interest collected during the past 30 days; b = accrued expenses of the past 30 days; c = average daily number of outstanding shares that were entitled to distributions