RatedrillAnnuity due
An annuity due is a series of equal payments made at the start of each period, like rent or a lease. Because every payment comes one period earlier than in an ordinary annuity, its present value and future value are the ordinary annuity values multiplied by (1 + r). In Excel set type to 1.
Syntax
PV_due = PMT x (1 - (1 + r)^-n) / r x (1 + r) FV_due = PMT x ((1 + r)^n - 1) / r x (1 + r)| Part | What it is |
|---|---|
PMT | Payment per period, made at the start |
r | Rate per period |
n | Number of payments |
Examples
FV of 100 per year for 3 years at 5%, paid at the start
FV = 100 x (1.05^3 - 1) / 0.05 x 1.05Result: FV = 331.01 (ordinary annuity: 315.25)
Excel: =FV(5%, 3, -100, 0, 1)
PV of a lease: 1,000 per month for 12 months at 0.5% monthly, paid in advance
PV = 1,000 x (1 - 1.005^-12) / 0.005 x 1.005Result: PV = 11,677.03
Excel: =PV(0.5%, 12, -1000, 0, 1)
PV of 100 per year for 3 years at 5%, paid at the start
PV = 272.32 x 1.05Result: PV = 285.94
Common mistakes
- Treating rent or lease payments (paid in advance) as an ordinary annuity understates their value by a factor of (1 + r).
- Leaving the Excel type argument blank or 0 for begin-of-period payments; type 1 is required.
- Multiplying by (1 + r)^n instead of (1 + r): the whole stream shifts by only one period.
Practice Annuity due
These drills check your answer on live data, free, no account needed.
- Annuity due: deposits at the startYou put $1,000 into a retirement account at the start of every year for 35 years. It earns 4.25% per year. What is the balance at the end of year 35?
- Annuity due: value of a leaseA tenant owes $800 rent at the start of each month on a 12-month lease. At a discount rate of 10% APR, compounded monthly, what is the present value of all the rent?
Questions
Is an annuity due worth more or less than an ordinary annuity?
More, by a factor of (1 + r), because each payment arrives one period sooner and so is discounted less (or earns interest longer).
What are real examples of an annuity due?
Rent, lease payments, insurance premiums and savings deposits made on the first of the month are annuities due. Loan repayments and bond coupons are ordinary annuities.
Related
- Annuity formula (future value)The future value of an ordinary annuity is PMT x ((1 + r)^n - 1) / r. Examples for yearly and monthly deposits, the Excel FV function and common errors.
- Present value of an annuityHow to find the present value of equal payments with PV = PMT x (1 - (1 + r)^-n) / r. Worked examples, Excel PV and why this is the loan formula in disguise.
- PerpetuityA perpetuity pays a fixed amount forever and is worth PV = C / r. The growing perpetuity formula C1 / (r - g), examples for preferred stock and dividends.
- Monthly deposit for a savings goalThe monthly deposit needed to reach a target is PMT = FV x r / ((1 + r)^n - 1). Examples for 10,000 in 5 years and 50,000 in 10 years, Excel PMT and errors.