Math Quiz Answers

These are the answer to my Millionaire Math post from last week. How did you do? Let’s take a look…

#1

Let’s start simple, just for a warm up. You have a savings account paying 1% annual interest and you put a $1,000 into the account. How much money would be in the account after 2 years if the money and the interest remained constant?

A lot of folks got this one right, but the most common wrong answer factored as if it was a simple 2% interest paid 1% each year on the $1,000 principal. However, the interest compounds. Year one would end with 1% on $1,000 ($1,010) and year two would end with 1% interest on $1,010 or (the answer) $1,020.10

#2

Here’s another easy one. I like cheese. I like really good and expensive cheese. Stored properly, cheese will safely last 3 months. Let’s say my family eats a pound per week. One day we go into the grocery store and I notice cheese on sale at 50% off – the cheapest I’ve ever seen it. What a deal! How much cheese should I buy?

Easy one – if you are eating 1 pound per week or 4 pounds per month, and it will keep for 3 months, you should buy 12 pounds. Most folks may doing their shopping may say “ok cool… half off” and buy an extra pound or two, but you need to leverage these deals to the max! I recently saw my favorite dark chocolate bars on sale for 50% off at Kroger. The “sell by” date was late 2021. I bought all the store had in stock. This is a very effective way of lowering your grocery bill.

#3

Is a $60/year Costco membership worth the money for the gas alone? You’ll save 20 cents per gallon, your car gets 30mpg, and you drive 10,000 miles per year.

At 30mpg you’ll need roughly 333.33 gallons to drive 10,000 miles. Saving 20 cents per gallon means (333.33 x .2) or $66.67. So yes, the Costco membership would pay off, and you’ll be roughly $7 to the good. Treat your family to the Costco Food Court hot dogs for a “free” dinner!

#4

Leasing a car is about as poor of a financial decision as you can make, but what about leasing equipment for your business? Let’s say you want to open a technology-based company which means you’ll be buying a lot of computers and buying them often. You’ll always need the most current model to do your job well. You have a choice to lease $30,000 worth of computers for 3 years at $750/month or you can plunk down the $30,000 today and just bank on trading them in when you need new ones 3 years from now. Is this a good deal?

I like this deal. For $30,000 in equipment you will pay $750 x 36 or $27,000. That’s a 10% discount versus buying outright plus I don’t have to depreciate the gear – I can straight-line expense it (consult your CPA!). This frees up my cashflow for other business needs and I don’t have to worry about trade-in values moving against me.

#5

Your student loan is at 7% interest. It seems everyone is making money in the stock market these days, so you decide to make minimum payments on your loan in exchange for investing some of your extra money in the market. You reason you can take your gains and use them to pay the loan later. In addition, you hate to miss out on a hot stock market when all your friends are bragging about how well their investments are doing. With your loan at 7%, the risk-free rate at 1.5% (T-bills) and the stock market’s Implied Rate of Return currently at 8.1% (S&P500) is investing in the stock market wise? Or should you forgo investing in stocks and pay off the loan?

When the risk-free rate is 1.5% ands the market’s IRR (Implied Rate of Return) is 8.1%, that means you are seeing a (8.1 minus 1.5) 6.6% risk premium for investing in stocks. If your loan is at 7% you are far better paying off the loan. That’s essentially guaranteeing you a 7% return on your money. More info here.

#6

You have 2 credit cards, Card A carries a $5,600 balance and Card B carries a $7,200 balance. Card A is at 12.5% interest rate and Card B is at 14.6% interest rate. You’re currently only making minimum payments, but you can qualify for a home equity loan with less than 6% interest and get the $12,800 to pay off your credit cards. Closing costs on the home equity loan will run $300. Should you do this deal?

There is nothing relevant here in terms of interest rates, card balances, or closing costs. Never take unsecured debt and convert it into secured debt against your home. Never. If you secure the undies you bought on your Victoria’s Secret credit card against your house, you are a special kind of crazy.

#7

You decide to become a landlord and invest in rental property. You buy a house for $250,000 that you can rent for $1,750/month. You’ll pay a property manager $900/year to manage your tenants, spend $1,500/year in maintenance & lawn care, $1,400/year in taxes, and $1,200/year in insurance. With a positive cashflow of $16,000/year this sounds pretty good – you’re on your way to becoming a real estate king! Is this a good rental property?

The easiest way to figure the return on rental property is to determine the capitalization rate on your capital (or cap rate). This is done by dividing your annual cash flow by your initial investment (16,000 / 250,000 = 6.4%). Is this a good cap rate on rental property? It’s decent on a low-risk and in demand property, but most real estate investors would look for a 7-10% cap rate. I do not like this real estate deal. I’d take the 6.6% risk premium in the stock market (see #5) over the 6.4% cap rate on the rental. A lot of folks are blinded by the income on rental property investment without factoring in a true capitalization rate on their money.

#8

Conversely you take a new job in a new city. The houses in the neighborhood where you want to live run $550,000. You have a considerable amount of cash in the bank from the sale of your previous home. This means you can afford a very large down payment but you also notice you can rent for $2,400/month in the same neighborhood. Looking long term should you go ahead and buy a home, or should you rent a home and invest your money in the stock market instead?

There are a lot of “rent vs buy” calculators that will help you with this decision, but the quick math is to look for a price/rent ratio of 200 to 220. Below that and buying looks like a better deal. Much above that and you should probably rent. In this example 550,000/2,400 = 229 so you should seriously consider renting. It’s not a popular answer, but math usually wins. Real estate values are sky high and with home ownership comes taxes, insurance, maintenance, an interest rates on a mortgage. There are many instances where renting may easily make more sense. Don’t fall into the age old adage that rent is just “throwing your money away”. There are other factors at play.

#9

You need a new HVAC unit that is going to cost $8,295. Your contractor will knock $150 off the bill if you pay with cash, which you have readily available. However, you’d like to use your Southwest Visa to earn the mileage points. What is the better deal?

Southwest points are worth about 1.5 cents each as of early 2020. So 8,295 x .015 = $124 worth of points. Pay cash and let the contractor knock off the $150. You will come out ahead by $26. I wonder how many people overestimate the value of those “free” miles? Don’t forget you also pay Visa $75/year for the ability to accumulate points.

#10

You have the opportunity to invest in a business. The owner is asking for $5,000 and he will pay you back $6,000 over the next 3 years ($1,000 in year one + $2,000 in year two + $3,000 in year 3). Is this a worthwhile investment?

Tricky one… Remember, inflation runs around 2%. Money made 1, 2, and 3 years from now will be worth less than it is today. To look at this investment you need to discount the future cash by inflation (2%) and then calculate the risk premium you want to see (I’d want to see lat least 7% since I can get 6.6% in the stock market, see #5.) That means a total discount of 9%. You will need the exponent button on a calculator (xY) – that’s the button you used in junior high algebra! You will raise 1.09 (your discount) to the power of 1, 2, and 3 to represent the time factor. You can do this in a spreadsheet as well, but if you do the math you will find the present value of the cash flows over the next 3 years is $4,917 which is less than the $5,000 investment. Do not do this deal.

#11

You’re 35 years old and have no savings for retirement yet. You decide to get serious since you want to retire at 70 and live on something more than social security income. Currently your budget is $5,000/month. How much should you start saving in order to maintain a similar level of income while resting comfortably on the beach in Del Boca Vista in 35 years?

A lot of moving pieces in this one. First, if you need $5,000 to live today and inflation runs 2%, you need to use the rule of 72 to see when prices will double. 72/2 means 36 years – which means you will need around $10,000 a month to retire in 35 years to live like you do today.

Second, if SS pays, on average, around $2,000/month now and you expect the program to be around in 35 years, you’d probably see $4,000/month using the calculation – and assuming Uncle Sam is still in business by then.

That means you will need roughly (10,000-4,000) $6,000/month or roughly $72,000/year from your nest egg. Since you want to limit withdrawals on your nest egg to around 5% to ensure its sustainability this means you will need at least (72,000 / .05) or $1.44M to retire comfortably.

So now, head to a retirement calculator like Dave Ramsey’s which is incredibly easy to use. I estimate you will need to save $650/month and earn an average of 8%/year to get to that $1.44 million. Time to get busy!

By the way, if you want to factor out Social Security (which may be prudent), that means you will need $120,000/year in retirement so 120,000/.05 = $2.4M next egg or around $1,100/month earning 8% on average over the next 35 years. Ouch! This illustrates the importance of saving for retirement as early as possible. Do not wait!

#12

You’ve inherited $100,000 from dear aunt Sue. You’d like to invest it in something with guaranteed returns, so CDs earning 3% sound good. How long will it take for your inheritance to double in value?

Again, the rule of 72 is your friend. Divide 72 by your expected rate of return to find out how many years your money will take to double. 72/3 means it will take 24 years for your investment in 3% CDs to double in value. Turn around and earn 8-10% on average in the stock market and your money doubles in 7 to 9 years. That sounds better – way better than 24, but with more risk.

Ok… how did you do? Hopefully this gets you thinking and applying the rules of math to investing and personal finance situations you’ll see on a regular basis.

For my next blog I think I will take a look at the Corona Virus – until then, cheers – and thanks for reading!

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