Ever wonder why a 3-year car loan has a higher payment than a 5-year one?
Or why subscriptions offer discounts if paid in advance for the year?
The answer is a fundamental concept in finance: “time value of money”. 
Learning it allows you to compute the value of a series of transactions that stretch across time, translated into a single price.
Or, you can go the opposite way and translate a current price into a series of payments that have equal value.
Imagine I offer you a choice: would you rather have $100 today, or $100 one month from now? Of course we prefer the immediate payment rather than waiting.
But why?
Waiting to get paid means missing OPPORTUNITIES to enjoy the money.
Maybe there’s an event you want to attend – a football game perhaps. If you had the money today, you’d buy a ticket. But let’s say you wait to get the $100 and the season ends before you can buy the ticket.
You didn’t physically pay any money (you still got the $100). But you missed something you would’ve enjoyed.
This “opportunity cost” is real and the way you measure it is with interest rates.
Interest rates are simply “the price of time””
h/t @chancellor_e 
How much MORE do you need one month (or one year) from now to make waiting to get paid worth it vs. getting paid today?
I’ll sweeten the deal, how about I give you $101 next month, OR $100 today – which do you choose?
What if you took the $100 today and INVESTED IT in a high yield savings or money-market account?
http://bankrate.com shows many money markets currently paying 4.5% to 5%. Interest rates on savings accounts is typically stated in annual terms…..
Annual rate (5%) divided by 12 = monthly rate.
5 /12 = 0.42. The current one-month rate of return THE MARKET offers you on idle cash is 0.42%
Compare this to my offer ($101 if you wait a month).
1/100 = .01. The one-month rate of return I’m offering is 1%
My offer wins
In dollar terms, you can
A: take $100 today, invest it at 0.42% for a month, end up with 100 * 1.0042 = $100.42
B: wait one month, collect $101
Option B is better because
1 – we end up with more money
2 – we earn a higher interest rate
Two ways to evaluate it
This is a simple, hypothetical example. A one-month return of 1% equates to an annual return of 12%.
US stocks returned an average of 10% per year over the last 100 years. 12% is a high return, and likely I’m taking significant risk to get it. Risk & return are always linked …
What if I change my offer: $100 today or $101 in ONE YEAR?
Which is better?
A – Market return on cash is ~5% per year. Take the $100 now, put it in savings, end up with 100 x 1.05 = $105 in one year.
B – Receive $101 in one year. $1 on a $100 investment = a 1% return.
Clearly option A is better.
This is the math companies do when they price goods and services. Often getting paid today is better than getting paid in the future.
⬆️ market rates = more attractive investments can be made NOW, which makes 💵 today more valuable.
To end, let’s look at a real-world example.
offers online video guitar lessons via subscription. Customers have two payment plans to choose from: $29 per month or $124.50 per year. Let’s compare 🧐👇 Truefire.com
To evaluate streams of payments it’s best to use a financial calculator (many free ones online). There are five variables involved:
– number of periods (n)
– interest rate (i)
– present value (PV)
– payment amount (PMT)
– future value (FV).
Monthly plan:
n = 12 (monthly payments)
i = 0.42 (market interest rate, 5% / 12 = 0.42%)
PV = 0
PMT = -29 (we are paying the money, so the sign is negative)
Enter in the first four variables and the calculator computes the last one …
FV = 356.15
What does it mean? 👇
If we paid $29 per month for 12 months into an investment offering a 5% annual return (.42% monthly), at the end of that period we would have $356. This is what we give up (opportunity cost) by choosing the monthly plan.
Let’s compare vs. the yearly plan …
Yearly plan:
n = 1 (one year)
i = 5 (annual rate = 5%)
PV = -124.50 (we are paying the $124.50 today)
PMT = 0
(calculator computes …)
FV = 130.73
@chancellor_e $124.50 invested for one year at 5% grows to $130.73 at the end of the period. This is our opportunity cost for the annual plan.
Annual plan is a much better deal for the CUSTOMER in this case.
So why does the company offer an annual plan if they make more on the monthly?
Monthly plan customers can cancel during the year. Let’s say someone cancels the monthly plan after 3 months:
n = 3
i = 0.42
PV = 0
PMT = -29
(calculator computes …)
FV = 87.37
The monthly plan is only more profitable if the customer holds it for at least 5 months.
From the COMPANY’S perspective:
Profitability of the monthly plan is higher after 5 months, but ability to cancel makes those profits more uncertain.
Annual plan is less profitable, but the level of profitability is more stable (can’t cancel in the middle of the year).
That’s a wrap! If you enjoyed this, please
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