*Today’s post is from Michael who blogs over at Stretch a Dime. You might remember Michael guest posting here a few weeks ago about the Time Value of Money. This is part 2 – an extract taken from Michael’s book. Get your calculators (or Excel spreadsheet) at the ready! Hope you find this post useful – please head on over to check out Michael’s book and blog after reading this post!*

In my earlier post, I had explained the very basics of the time value of money. Now that you understand the time value of money, let’s take it up a notch. Let me illustrate how you could use the concept of the time value of money in a car purchase scenario.

### A car purchase scenario

You are interested in purchasing at car for $20,000. The questions is should you be paying cash down or should you finance it? What if you already had the $20,000 in cash? What would you do then? There’s a lot to be said about owning a big ticket item free and clear, and let me tell you, it feels good not having to make that monthly payment.

Does it make more sense to pay for the car outright and not have to worry about making a payment, or is it smarter to invest and potentially earn interest?

Let’s dive right in!

You need to ask yourself the following questions:

- What is the loan interest rate?
- What is the total interest I will be paying on the loan?
- If paid in full with cash, how much can I save?
- If I choose to go with a loan and invest the cash, would it give a better return?

**You then need to compare the cash values at the same point in time and decide which option is better.**

So, if our $20,000 car loan carries a 3% interest rate for 60 months (5 years), but we’re also able to earn 3% per year in a CD for 5 years, the math on our options would look like this:

### Option A – finance & invest

Let’s look at financing aspect of the car first:

Finance Car Sale Price $20,000 @ 3% / year for 5 years. We know the price, interest rate, and term. With this, we can calculate the monthly payment.

In an Excel cell, type “=PMT(0.03/12,60,20000)”, and you will get -$359.37. The sign is negative, because that is the amount you will be paying every month for the next 60 months.

**Total Cost = $359.37 * 60 = $21,562.43** ($20,000 Principle + $1,562 Interest). The total cost is the total amount paid over a 5 year period.

Let’s now look at the investing aspect:

$20,000 Invested Cash in 5 year CD @ 3% / year for 5 years.

In an Excel cell, type “=FV(0.03/12,60,0,-20000)”= $23,232.34.

If you invested $20,000 in a 5 year CD @ 3% / year, you will have a total of** $23,232.34.**

At the end of five years, $23,232 (FV) – $21,562 (Total Cost) = **$1,670 Cash in Hand.**

### Option B – pay cash

Car Sale Price: $20,000 paid upfront in cash = **Total Cost $20,000.**

You have $0 left to invest. Hence, Future Value (FV) = $0.

Therefore, after 5 years, because we did not invest anything, we have **$0 Cash in Hand.**

This means if we took out a car loan at 3% and we are able to invest our money at 3% over the same timeframe, we would end up with $1,670 at the end of 5 years. If you paid in cash and did not invest at all, because there is nothing left to invest, you would have $0 left after the 5 year period.

It may all seem a little obvious, but what I just told you is that it is not always better to be debt-free, as you can see above. With an equal loan interest rate and a compound interest rate over the same period, you will always come out ahead by investing over paying cash, assuming your investment turns a profit. That’s the key.

There is risk associated with every financial decision you make. When it comes to buying a car, here is my opinion: we believe in frugal living. Buy a good, safe, reliable, and cost-optimized car; evaluate your payment, investment choices, and associated risks.

Understanding the time value of money and applying it practically in daily life is the first step toward adopting a wealthy state of mind.

(*An extract from the book “**High School Money Hacks**”, slightly modified to turn it into a blog post).*

___________________________________________

**Author Bio:** K. Michael Srinivasan, author of personal finance blog Stretch A Dime, where he writes about Personal Finance, Investing, and Frugal Living.

**Images courtesy of Pixabay – text overlay added.*

By subscribing, you'll receive new blog updates by email and occasionally I might email you with any exciting news. I promise not to spam you and your details will never be passed on.

Emily says

I see your point, but it looks like you’re ignoring the money you would be spending on the car payment. Assuming you paid cash but still paid a 357.39 car payment into the same investing tool each month, you wouldn’t have $0 at the end of five years.

The way you’re looking at it, I guess you’re assuming you’re not saving or investing the difference. If you were, then it works out to about the same. However, it’s riskier to pay cash as you don’t actually have the money to fall back on if needed.

Michael says

Hi Emily,

Good point, great observation, you are correct. I wanted to explain the thought / approach that needs to be taken before any spending decision.

If both the loan interest rate and the bank savings account interest rate are the same, then you don’t gain anything by paying cash down. You have cash to fall back on.

–Michael

Femme Frugality says

I was going to say the same thing! Appreciate the sentiment, though.

Femme Frugality recently posted…Financial Psychology Worth Sharing

Michael says

My personal finance decisions are very objective. If I can get better returns on my money and borrow at a lower rate for a purchase I am making, I will usually take the route of borrowing money for the purchase even though I could pay cash down.

Michael recently posted…How To Wire Money

Jayson @ Monster Piggy Bank says

Michael, you have a good point. I agree with you that investing some of the money can be advantageous, based on your calculation. But, I think the outcome is still dependent on your investing strategies. Still, I’d go for option A.

Jayson @ Monster Piggy Bank recently posted…Splitting the cost of a vacation

Michael says

Hi Jayson,

You are correct. The key take away is to look at both options A and B, do you own evaluation, and make a conscious decision based on your analysis.

A lot of people want to be debt-free and may end up making poor financial decisions by completely ignoring the time value of money.

–Michael

Michael recently posted…How To Wire Money

Kathryn @ Making Your Money Matter says

Time value of money is a tricky topic. Inflation definitely comes into play here as well with the car financing example. I’d rather be debt free, but that’s my preference!

Kathryn @ Making Your Money Matter recently posted…Tracking Your Debt Goals

Michael says

Hi Kathryn,

I certainly understand your preference. Time Value of Money very logical and objective.

Every act of spending is financed. You finance your purchase yourself or you borrow money. If you finance it yourself, then it could be lost opportunity – the lost opportunity of not investing the money. If you borrow, then you are paying an interest on it.

If you pay cash down, you need to evaluate the lost opportunity. If you could get a better return investing the money, and get a loan for a lower rate, you get to keep the spread.

–Michael

Michael recently posted…How To Wire Money