You are offered two options: $5,000 today, or $5,500 one year from now. The going interest rate is 8% per year. Which option has higher financial value?
A$5,000 today — money now is always better than money later
B$5,500 in one year — it's a larger number so it's worth more
C$5,000 today — investing it at 8% gives $5,400, which is more than $5,500
D$5,500 in one year — its present value ($5,500 / 1.08 ≈ $5,093) exceeds $5,000 today
To compare, discount the future $5,500 back to today: $5,500 / 1.08 ≈ $5,093. Since $5,093 > $5,000, the future option is worth more in today's terms. Alternatively: investing $5,000 at 8% yields only $5,400 in one year, which is less than $5,500 — confirming you'd rather wait. Option A ('money now is always better') is a common heuristic that fails here: time value of money cuts both ways. Option C makes a correct comparison but draws the wrong conclusion — $5,400 < $5,500 means the future option wins.
Question 2 Multiple Choice
A lottery advertises a '$20 million jackpot' paid in installments over 25 years. The lump-sum cash option is $12 million. The gap between $20 million and $12 million is primarily explained by:
ALottery administrative fees and commissions taken by the state
BThe time value of money — future installments are worth less today than their face value
CTaxation — the government withholds the difference before paying the winner
DRisk — there is a chance the lottery will default on future payments
$20 million paid over 25 years has a present value far below $20 million, because each future payment must be discounted back to today. At typical discount rates, the present value of that stream of payments is roughly $12 million. This is discounting in action: a dollar promised in year 25 is worth much less than a dollar today because the dollar today could be invested and compounding for 25 years. The lump-sum option gives you the present value directly.
Question 3 True / False
The time value of money only applies when inflation is present — in a zero-inflation environment, $1 today and $1 in the future are equally valuable.
TTrue
FFalse
Answer: False
The time value of money exists independently of inflation. Even in a zero-inflation world, a dollar today is worth more than a dollar in the future because you can invest it and earn a return. The opportunity cost of waiting — the returns foregone while holding a future claim — is what drives the time value of money. Inflation amplifies this effect but is not its cause. Even a guaranteed 0% inflation economy would still have positive real interest rates as long as there are productive investments.
Question 4 True / False
Investing $10,000 at age 25 rather than age 35 — with no additional contributions — produces significantly more wealth at retirement due to compounding.
TTrue
FFalse
Answer: True
At 7% annual growth, $10,000 invested at 25 grows to roughly $160,000 by age 65 (40 years of compounding). The same $10,000 invested at 35 grows to only about $76,000 by age 65 (30 years). The 10-year head start more than doubles the outcome — not because of the additional years themselves, but because compounding is exponential. Early years generate the base on which all subsequent compounding builds. This is why small differences in timing compound into large differences over decades.
Question 5 Short Answer
Explain what 'discounting' means in the time value of money framework, and why it is conceptually the reverse of computing future value.
Think about your answer, then reveal below.
Model answer: Future value asks: if I invest PV today at rate r for n periods, what do I accumulate? FV = PV × (1+r)^n. Discounting runs the formula backward: given a future amount FV promised in n periods, what is it worth to me right now, given I could earn r elsewhere? PV = FV / (1+r)^n. Discounting 'shrinks' a future sum to its present-day equivalent by removing the returns it could have earned. If you could earn 5%, a promise of $1,200 in 3 years is worth $1,200 / (1.05)³ ≈ $1,037 today — because $1,037 invested now at 5% would reach exactly $1,200. Any offer priced above $1,037 for that future $1,200 is a bad deal at a 5% discount rate.
This present-value comparison is the underlying logic of every financial decision involving future cash flows: mortgages, annuities, lottery payouts, salary negotiations with deferred bonuses, and investment returns. Once you can discount, every offer involving future money has a comparable today-price.