Time Value of Money

The two translations

The time value of money lets you move dollars through time in either direction.

Future value (FV) tells you what today's money becomes later. $1,000 invested at 7% for 10 years has a future value of about $1,967.

Formula: FV = PV × (1 + r)^n

Present value (PV) tells you what future money is worth today. $1,000 you'll receive in 10 years, discounted at 7%, has a present value of about $508.

Formula: PV = FV / (1 + r)^n

The variables:

• PV = present value (dollars today)
• FV = future value (dollars later)
• r = interest rate per period
• n = number of periods

Why this matters

Retirement savings targets. If you need $80,000/year in retirement spending starting in 25 years, inflation of 2.5% means you'll actually need about $149,000 in year-25 dollars to buy what $80,000 buys today. Planning against today's number would underfund retirement by nearly half.

Evaluating offers. A job offer of $120,000 today vs $150,000 signing bonus in year two vs $180,000 salary in year three isn't a simple addition. Each payment has a different present value depending on your personal discount rate.

Buying vs leasing vs financing. The "cash price" of a car and the "monthly payment" are apples and oranges. Converting both to present value is the only way to compare them honestly.

The discount rate

The discount rate (r) is the rate at which you trade off present and future. Small changes have massive effects over long horizons:

• $1,000 in 30 years at 3% discount = $412 today
• $1,000 in 30 years at 6% discount = $174 today
• $1,000 in 30 years at 9% discount = $75 today

Choosing the discount rate is where most time-value disagreements happen. Common choices:

• Inflation rate (typically 2–3%) if you want to know real purchasing power.
• Risk-free rate (10-year Treasury yield) if comparing to the safest alternative.
• Expected portfolio return (typically 5–8%) if comparing to what you could otherwise earn.
• Your personal hurdle rate — the minimum return you'd accept to take on risk.

Annuities

An annuity is a series of equal payments. The present value of an annuity is the sum of the present values of each payment, and it has a closed-form formula:

PV = Payment × [1 − (1 + r)^−n] / r

This is the formula behind mortgage payments, pension valuations, and annuity pricing. A $2,000/month mortgage for 30 years at 6% has a present value of about $333,500 — meaning a $333,500 mortgage generates that payment stream.

How Horizons uses this

Every dollar in Horizons is tracked in nominal terms (actual future dollars), but the engine applies inflation to expenses so you can compare across years on an apples-to-apples basis. When we report your retirement readiness score in today's dollars, we're using present-value math to translate your future balance into something you can compare to current income.