Can it be cheaper to borrow than save?

C

Cabaiste

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I'm currently looking to buy a new car. I have savings of 13,500 which I was going to use but have being doing some figures which seem to suggest that it would be cheaper to borrow and keep my savings in the bank can this be right?

Here are the workings I am basing this on.

Loan Rate = 7.49% available from local credit union
Savings Rate = 4.3% with rabo Direct (3.44% net of DIRT)
Repayments on 13,500 @ 7.49% over 3 years = 419.81 per month.

Cost of Borrowing
Interest on Loan (13,500 @ 7.49% over 3 years) 1,615.39
Less interest earned on savings (13,500 @ 3.44% for 3 years) (1,442.00)
Total Cost of Borrowing 173.39

Cost of Using Savings
Oportunity Cost (ie Interest on savings above) 1,442.00
Interest earned on Saving "Notional" Pmnts (783.51)
Total Cost 658.49


Is there something I am leaving out? Doesn't Eddie Hoobs always say its crazy to borrow at a higher rate than your savings are earning?
 
"Interest earned on Saving "Notional" Pmnts (783.51)"

I wonder could you explain what this means ?
Thanks
 
also how can.. Interest on Loan (13,500 @ 7.49% over 3 years) = 1,615.39
and interest earned on savings (13,500 @ 3.44% for 3 years) = 1,442.00 (when the rate on the loan is nearly twice the rate on the savings) ?
 
huskerdu:

The repayments on the loan would be 419.81 per month. If I were to save this money in the Rabo account @ 4.3% then the total interest earned over 36 months would amount to 783.51!

stephnyc:

Interest charged on the loan is charged on a reducing balance so is getting smaller and smaller each month.

Interest earned is compounded monthly so you earn interest on top of interest!
 
What you are missing is the difference is what you will have in 3 years time, when the loan is paid.

In scenario 1, you pay out approx 419.81 per month on the loan, and after 3 years you then have
savings of 13500 + 1442 = 14942

In scenario 2, you save 419.81 per month and after the 3 years you have 419.81 * 36 = 15113.16 before
interest is added, which another few hundred, at a very rough calculation. This cancels out the extra "cost"
and makes it better value.
 
Last edited:
huskerdu said:
interest is added, which another few hundred, at a very rough calculation. This cancels out the extra "cost"
and makes it better value.
Click to expand...

I have accounted for this. The interest earned on the 419.81 pm amounts to 783.51!
 
OK, I think I have it straight now. Both options have an opportunity cost. I was only considering the opportunity cost of spending / keeping the principal but not the opportunity cost of using the monthly loan payments as savings!

My revised workings are as follows. (I've used total cost this time as I think it makes it easier to understand!):

Use Loan
Cost of Car 13,500.00
Int on Loan 1,615.39
Interest Earned (1,465.42)
Opportunity Cost 783.51

Total Cost 14,433.49

Use Savings
Cost of Car 13,500.00
Int on Loan 0.00
Interest Earned (783.51)
Opportunity Cost 1,465.42

Total Cost 14,181.90

So the difference is only €251 which over 3 years works out at only €7 per month!
 
That is why it is a good idea to only make comparisons based on APR for loans and CAR for savings.

If the cost of borrowing,APR, is higher than the rate of interest on deposit, CAR, you are losing money every year.

There is no need to complicate matters with repayments, total cost of credit, opportunity cost etc. Look at it on an annual basis - If I borrow €100 at 5%, it will cost me €5. If I place that on deposit at 2%, I will earn €2. At the end of the year, I will have lost €3.
 
Because of the time value of money, you can't add all those figures together; it's comparing apples with oranges. The cost of the car is only relevant for interest purposes, so I don't think you need to include it in your sum.

I think it's less confusing to look at your position at the end of the loan period, as huskerdu suggests.

Money in your pocket after loan period

If you borrow to buy you
- keep €13,500 lump sum you started with
- earn [broken link removed] on the lump sum @ 3.44% net which brings total to
€14,941.68


If you spend your lump sum ("Brendan's advice") you
- save your repayments of €13,500 @ 7.49% over 3 years = 36 x €419.87 coming to
€15,115.32
- earn [broken link removed] @ 3.44% net which brings total to
€15,931.19


In both cases you
- have the same car at the end. The value of the car (now or after 3 years) isn't relevant.
- pay out €419.87 each month, to your lender or your savings account. The hypothetical foregone savings interest on loan repayments or lump sum are irrelevant; there are no opportunity costs.

It should be possible to get more than 3.44% net on savings, particularly if you are saving regularly (e.g. instead of making loan repayments!). If we assume a more realistic 5% net on regular savings, using your savings to buy the car comes out even further ahead at €16,310.66. Even if you earn no interest on your savings, you still come out ahead!


Non-monetary factors

You might prefer to borrow
- it gives you more flexibility should your lose your job part-way through repaying the loan (e.g. if you have no income for 3 months you won't be able to borrow money then, and could be glad that you haven't spent your savings.).
- loan repayments force you to be disciplined; you might not be as disciplined about rebuilding your lump sum with savings

You might prefer to spend your lump sum
- less risk if your savings institution goes bust
- a wayward spouse can't spend the tempting lump sum on something else! Ditto if you were to get divorced etc.
 

This doesnt take into account that interest is charged on a reducing balance while interest earned is compounded.

In your example above, if you borrow €100 @ 5% APR and pay it back in 12 monthly installments it will only cost you €2.73 in interest.

(Workings: Using MS Excel; formula is =pmt(0.05/12,12,-100) = 8.56 per month. 8.56 * 12 = 102.73 - 100 = total cost of finance = 2.73)
 
Cabaiste

That is why I strongly recommend using APR and CAR which are the true interest rates and take into account all factors.

Brendan
 
Cabaiste said:
I have accounted for this. The interest earned on the 419.81 pm amounts to 783.51!
Click to expand...

I still dont think you have done this correctly.

How have you calculated the 783.51 ? I think this is the 1024 interest that the radodirect website quoted minus DIRT.

According to the rabodirect website, if you save 419 a month for 3 years,
you earn 1024 interest ( 783 after DIRT) and have a total of 15896 at the end of the 3 years.

This is quite a bit more than the 14942 you have, if you invest the 13500.

you still have not factored in that 419 * 36 is a lot more than 13500
 

Something doesnt make sense about this.
 
That is why I strongly recommend using APR and CAR which are the true interest rates and take into account all factors.
Click to expand...

Actually, they don't take into account tax - e.g. mortgage interest relief or DIRT/PRSI on savings. But they are a very good rule of thumb.

Update: I've fleshed out the calculations in my first post, and borrowing leaves you €1000 worse off. Assuming I haven't missed anything. Reading Huskerdu's post(s) in more detail, (s)he comes up with a similar result.
 
The way I see it is:

If you leave your savings and borrow the net interest cost as you say is €173.39 over 3 years.

If you use your savings you won’t have to pay this €173.39, you own the same car, therefore this is the cheaper option. Is it not as simple as that ? as everything else is notional.
.
 

This was why I was considering using my savings. Lump sum was built up more through not spending bonueses etc than regular savings!

MugsGame said:
You might prefer to spend your lump sum
- less risk if your savings institution goes bust
- a wayward spouse can't spend the tempting lump sum on something else! Ditto if you were to get divorced etc.
Click to expand...

Divorced; would be some sort of record for shortest marriage in history; only married since October!!

The main reason I wa considering borrowing is that the money saved is money we intended to use for a deposit on a house (when the right one comes along!). If I were to use this money it would essentially be the same as paying for the car through the mortgage as I would have to borrow 13,500 more on the mortgage. The car would be long gone before the mortgage is repaid.

I was just playing around with the firgures when I saw that it may be cheaper to borrow and thought it couldn't be right.

Of course what I wasn't factoring in was as it was said here that the 419 per month is more than the 13,500 and I was only allowing for the interest earned in my calculation!

Thanks for everyones responses!
 
Cabaiste said:
Divorced; would be some sort of record for shortest marriage in history; only married since October!!
Click to expand...

Sorry, not trying to jinx your relationship, I mean't this as a general point! Wasn't even aware you were married...
 
My instinct is that the OPs calculations are a bit like one of those trick mathematical things whereby people prove that 1+1=3.

If it sounds like a duck and looks like a duck and quacks, then it usually is a duck.
 
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