I'm having a problem putting my mathematics degree to good use. A friend of mine wants me to work out the following problem for him:
A motorbike costs £14,000. I will receive a "sweetener" from the motorcycle company of £550 if I take out any amount of finance (£14K, £10K, or £5K - they will give you £550 however much finance you take out.)
With 5.9% APR, he wants to know how much finance he can take out, so that the cost of the finance is mitigated by the £550 sweetener, i.e. the finance costs him nothing.
I came up with the following solution:
$5.9%$ APR is equivalent to $0.01616%$ DPR (daily percentage rate)
Hence your interest rate is 100.01616% per day, or 1.0001616 as a decimal.
So we can write $b(1.0001616)^{365n}$ to express the total amount you will be paying back based on the amount borrowed, $b$, for $n$ number of years.
If we subtract the original amount borrowed $b$ from this, we will have how much interest we are paying for the finance:
$b(1.0001616)^{365n}-b = b(1.0001616^{365n}-1)$
And we want this to be the same as the sweetener so it effectively costs nothing, hence:
$b(1.0001616^{365n}-1) = 550$
which when rearranged, gives me $b=2840$
However, when I use an APR calculator, I'm told if I borrow £2840 for 36 months at 5.9%, the cost of the loan is £265... not the £550 I was expecting it to be.
Can anyone tell me where my solution has gone wrong? any help is appreciated.
Thanks!
Doug
For 3 years the composite interest is 9.1%. If you finance £6040 you are going to pay £6590 in three years, paying £183.06 per month.