Mathematics and Statistics · Ch 10 — Insurance and Annuity
Annuity — Meaning and Types
Annuity — Meaning and Types
An annuity is the mathematics of regular equal payments — a recurring deposit, an insurance premium, a loan instalment, a pension. Every annuity formula is just compound interest applied to each equal payment and summed as a geometric series.
Annuity and its terms
An annuity is a sequence of equal periodic payments made at equal intervals of time. Let
- = the periodic payment (the size of each instalment),
- = the interest rate per period as a decimal (e.g. per annum ),
- = the number of payments (periods).
The payment period is the gap between successive payments; when it matches the interest-compounding period the standard formulae apply directly.
Immediate (ordinary) annuity vs annuity due
The one distinction that changes every formula
- Immediate (ordinary) annuity — each payment is made at the end of its period. (A loan EMI or a recurring deposit at month-end is of this type.)
- Annuity due — each payment is made at the beginning of its period. (Rent paid in advance, or a premium paid at the start of the year.) …
A sequence of equal payments at equal time intervals; is the rate per period (decimal) and the …
Payments made at the END of each period (e.g. a loan EMI, a month-end recur …
Payments made at the BEGINNING of each period; each value is the ordinary-annuity value because every payment earns one e …