Are my sums correct???

jonray

I am buying a car and need £8000. Do i use my own cash to buy it or get a four year loan? Look at the sums.

If I take a loan I keep my money in the bank and make £8000 * 4% for 4 years = £1385 compounded. I pay back Northern Rock £186.77 * 48 months = £8965. So the charge for credit is £965. So i make a net gain of (£1385-£965) = £420.

If I use my own cash I lose interest (4%net) on £8000 for 4 years = £1385.
I pay myself back at £167 per month (£8000/48months) into my savings account with a 4% interest rate thus gaining £661 in interest compounded. I am also £20 better off each month that the Northern Rock repayment so (because I am sad) I pay this into my savings account and end up with £1039 with compounded interest. So (£1039+£661)interest - £1385 lost interest = £315 gained interest.

My sums must be wrong. Please help......

dmg24

What is the APR on the Northern Rock loan?

grumbler

jonray wrote:

...I pay back Northern Rock £186.77 * 48 months = £8965. ......

This corresponds to 5.7% APR. You cannot be better off by borrowing at 5.7% and saving at 4%. Very simple ...

BigDunc

If you can borrow money for a lower APR than you can get on your savings then you will make money. This seems unlikely as NR must charge around the 6% mark? How did you work out the return on your savings? https://www.bankrate.com has a calculator that you can use to see how much a regular monthly deposit will grow into. The sums don't look right but it's too close to going home time to get my head around it.

jonray

Thanks guys for the replies. Yes, the savings rate is lower than the loan rate but i'ts just complicated a bit by the giving up of my £8000 capital to finance it myself. The compounded savings return were done via an online calculator.

tryhard_2

hello jonray, have you factored in tax on savings?

tomstickland

OK, I'm just doing some sums, but I think for a fair comparison you need to work out how much interest you will make if you save £186.77 * 48 months, not £167.

lotto-dreamer

I also wondered about the tax - but this is actually a very interesting question - can't wait for some mathematical genius/money wizard to give us the answer

..also what about inflation - and depreciation of value of car as an asset over four years

tomstickland

OK here's my sums.
Plan A:
Borrow £8K at 5.7% gross rate for 4 years. Make 48 payments of £186.78
Total paid back £8965.
Meanwhile savings at 4% net get from £8K to £9385.
At end you have gained 9385-8965 = £420

Plan B:
Pay for car outright.
Then pay £186.78 into savings account each month. At end of 48 months you will have £9924 in the savings account.
You have gained £1924

If you chose to only pay 8000/48 in then you will end up with £8855 at the end.

westernpromise

Case A: If someone gave you £8,000 and you put it in the bank and borrowed £8,000 to buy the car, your £8,000 will increase to £9,385 after 4 years and you will pay out 48 lots of £186.77 (= £8,965). So, net, you now have £420 if you deduct what what you paid out from you've now got.

Case B: If instead you used that £8,000 to buy the car and deposited those 48 lots of £186.77 in the bank, you'll earn interest on that rising balance. So after 4 years, you'll have £9,723 in the bank. Take away the £8,000 you spent to begin with and you have £1,723.

The benefit from using your own savings versus taking a loan is thus B minus A: £1,330.

To put it another way, if you repay yourself in such a way as to end up with the same net surplus of £420, you'd only have to pay about £161 a month into the 4% deposit account, because after 4 years, that amount will be near enough £8,420. Thus borrowing to buy the car makes it about £25 a month more expensive.

It could still be worth it: if £8,000 is your entire stash you might want to hold it back for emergencies. Or if the finance deal is from the car company it may include things like insurance, which you would have to buy anyway and should be factored in.

@ tomstickland: great minds think alike!

westernpromise

lotto-dreamer wrote:

I also wondered about the tax - but this is actually a very interesting question - can't wait for some mathematical genius/money wizard to give us the answer

..also what about inflation - and depreciation of value of car as an asset over four years

Interest rate quoted is presumably net of tax.

Depreciation is the same however he buys the car so it has no effect on economics.