Time Value of Money: Present Value, Future Value and Annuities Explained
By SimplyCPA · 24 October 2026
On this page (6)
- Big idea: Money available now can earn a return, so it's worth more than the same amount received later.
- Present value: Discount a future amount back to today — PV = FV ÷ (1 + r)ⁿ.
- Future value: Grow today's amount forward — FV = PV × (1 + r)ⁿ.
- Annuities: An ordinary annuity pays at the end of each period; an annuity due pays at the start, so it's worth more (× (1 + r)).
- On the exam: Bond prices, lease liabilities and long-term notes are all present values of future cash flows.
The idea in one sentence
₹1 or $1 you hold today can be invested and earn interest, so it is worth more than the same amount promised a year from now. Time value of money is simply the arithmetic for comparing amounts that arrive at different times.
Future value and present value
- Future value (FV) — what an amount grows to: FV = PV × (1 + r)ⁿ.
- Present value (PV) — what a future amount is worth today: PV = FV ÷ (1 + r)ⁿ.
Here r is the interest (discount) rate per period and n is the number of periods. The higher the rate or the longer the wait, the smaller the present value.
Future value: $5,000 invested at 6% for 4 years grows to $5,000 × 1.06⁴ = $5,000 × 1.262477 = $6,312.38.
Present value: $10,000 received in 3 years, discounted at 8%, is worth $10,000 ÷ 1.08³ = $10,000 ÷ 1.259712 = $7,938.32 today.
Annuities: a series of equal payments
- Ordinary annuity (in arrears) — payments at the end of each period. Bond interest is the classic example.
- Annuity due (in advance) — payments at the start of each period. Rent and many lease payments work this way.
Because each payment of an annuity due arrives one period earlier, its present value is the ordinary-annuity value × (1 + r).
$1,000 a year for 5 years at 10%.
Ordinary annuity factor = 3.79079, so PV = $3,790.79.
Annuity due factor = 3.79079 × 1.10 = 4.16987, so PV = $4,169.87.
Where the CPA Exam uses it
- Bond pricing — issue price = PV of the face amount + PV of the interest payments, both at the market rate.
- Leases — the lease liability is the PV of the remaining lease payments (see our leases notes).
- Notes with no or unreasonably low stated interest — recorded at present value, with interest imputed at a market rate (ASC 835-30).
- Capital budgeting in BAR — net present value and internal rate of return are built on the same discounting.
The exam usually gives you factor tables, so the skill being tested is choosing the right factor: single sum or annuity, ordinary or due, and the market rate rather than the coupon rate.
Practice MCQs
1. A company issues a 3-year, $100,000 bond paying 5% interest annually when the market rate is 6%. PV of $1 for 3 periods at 6% = 0.839619; PV of an ordinary annuity of $1 for 3 periods at 6% = 2.673012. What is the issue price?
(A) $100,000 (B) $97,327 (C) $102,723 (D) $83,962
Answer: B. Principal $100,000 × 0.839619 = $83,961.90; interest $5,000 × 2.673012 = $13,365.06; total ≈ $97,327 — a discount, because the coupon rate is below the market rate.
2. Which is worth more today at a positive interest rate: five $1,000 payments at the start of each year, or five $1,000 payments at the end of each year?
(A) Start of each year (B) End of each year (C) They're equal (D) It depends on the inflation rate
Answer: A. An annuity due receives every payment one period sooner.
Bond accounting is covered in full in our FAR long-term debt notes.