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➲ You are shopping for a car for $20,000, and

have enough money in your account to pay up 
front, but then your salesman says he can get 
you a low interest loan. He argues that if you 
do this and invest your $20,000 at higher inter-
est rate you will come out ahead.

➲ The salesman adds “You’d have a 2% fee,”

which would be $400 added to the total loan 
amount

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➲ How much is the total loan, fees included?

➲ What would be your monthly payment for this

➲ How much would you pay over the course of

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➲ P0 Is the starting amount of $20000+$400 loan fee=

➲ R is the Interest rate as a decimal= 0.025
➲ K is the # of times interest applied per period= 12
➲ N is Number of time periods passed= 3
➲ D is the regular monthly deposit

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➲ What would be your monthly payment be for

By using the loan formula 
and inputting what we 
know we can solve for D.

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1 Month payment= $588.77
12 months in a year x 3 years in the lease

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➲ You can put the $20,000 in your bank account

straight into index funds, averaging 5% annual 
interest rate (compounding monthly). How 
much would this investment be worth after 3 
years?

Inputting what we know and using the 
compound interest formula we can see that 
PN = $23229.44 after 3 years

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➲ If you invest the same payment you would have

been making (from part a) into index funds 
each month (earning 5% annual interest, com-
pounded monthly), how much would this fund 
be worth after 3 years?

Using the annuity formula because 
we will be making regular deposits 
and inputting what we know. 
P3=$22816.80 after 3 years.

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➲ Was the salesman right? Which option is

better? By how much would you come out 
ahead? Let's look at out finances after 3 
years.

When you take the loan you end up with $23,229.44 in your account 
after 3 years, but you spent $21,195.72 on a car. Leaving a $2033.72 
difference.

When you don't take the loan you are left with $22,816.80 in your 
account after 3 years, but you only spent $20,000 on your car. Leaving 
a $2816.80 difference.

It appears to be better if you pay the cash and save the $783.08.

Recommendation of a Strategy

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Loans Formula
Compound Interest Formula
Annuity Formula