credit card repayment

Don't schools teach anything these days, that people need web tools for everything? I really despair sometimes.

Provided all the relevant facts are available, it's straightforward.

Suppose the interest rate is 1% per month, and the minimum payment is

This phase lasts until the balance (after interest is added) drops to £100 or less, because that's the amount of which 5% is £5.

Suppose you start off with a £10k balance, then you simply need to work out how long it takes for £10k to decay to £100 or less. More precisely, it needs to decay to below £99.01.

That's like figuring out for which N it is the case that the Nth power of 0.9595 is just less than 1/99.01.

N = -log(99.01)/log(0.9595)

I get N2 (months).

Sure enough, £10k x 0.9595^112 = £97.51

Now we're into the next phase of the problem. Here, the balance reduces according to:

A0 = £97.51 A1 = A0x1.01 - £5 A2 = A1x1.01 - £5 A2 = A0x1.01^2 - £5x(1+1.01) AN = A0x1.01^N - £5x(1+1.01+1.01^2+...+1.01^(N-1))

This will be zero when A0x1.01^N = £5x(1.01^N - 1)/0.01

Altogether, you'll need 112+224 months, more than 11 years.

"Ronald Raygun" wrote

But when the balance gets down to (say) 20, won't you think "ah sod it, I'll pay off the lot instead of just 5pm"!!!

Possibly but excel doesnt have an 'ah sod it' function (AFAIK).

"Tumbleweed" wrote

Ah, but I happen to know that Ronnie doesn't "speak Excel", so that's irrelevant! :-)

To save circa 50p interest? When he's been deliberately wasting money for 11 years by choosing to pay as little each month as possible, i.e. by deliberately electing to pay the maximum possible amount of interest? Not very likely!