I'm in the process of upgrading my phone, and was just offered insurance against losing or damaging my new shiny. "It'll cost you £299 to replace your phone," it says, and offers me peace of mind for just £6 per month over my two year contract.
How much?
Seems reasonable, on the face of it. But let's do some sums, and not think about the fact that my home insurance payment is only double that.
Over the 24 months, with the insurance, I'd end up paying a total of £24 x 6 = £144: nearly half of the value of the phone. So, is it worth it?
Well, that turns into a probability question. The value of the insurance to me is how much the phone would cost to replace multiplied by the probability of me claiming on it. For instance, if I had a 1% chance of losing the phone over the next two years, the insurance would be worth about 0.01 x £299 = £2.99.
So, if I call the value V, the probability p and the cost of the phone C, the equation would be: V = pC.
That means, the policy is good value for me if I think I have a more than 48% chance of losing my phone over the next two years. And while I'm clumsy and forgetful, I've never lost or broken a mobile phone.
So, this policy is a really bad idea for me - I'd do much better to put £6 a month into a savings account and use it to buy something nice at the end of it: maybe a new phone!
Seems reasonable, on the face of it. But let's do some sums, and not think about the fact that my home insurance payment is only double that.
Over the 24 months, with the insurance, I'd end up paying a total of £24 x 6 = £144: nearly half of the value of the phone. So, is it worth it?
Well, that turns into a probability question. The value of the insurance to me is how much the phone would cost to replace multiplied by the probability of me claiming on it. For instance, if I had a 1% chance of losing the phone over the next two years, the insurance would be worth about 0.01 x £299 = £2.99.
So, if I call the value V, the probability p and the cost of the phone C, the equation would be: V = pC.
Should I?
That would be worthwhile if the value was greater than the cost of the insurance (I): V > I, and since we know V is the same thing as pC, I can replace that in the inequality:
Now, I know two of those values: C = 299 and I = 144, so, the policy is good value if:
Dividing both sides by 299 (inequalities work, for the most part, just like equals signs):
pC > I
Now, I know two of those values: C = 299 and I = 144, so, the policy is good value if:
299 p > 144
Dividing both sides by 299 (inequalities work, for the most part, just like equals signs):
p > 144 / 299 ~ 0.4816.
That means, the policy is good value for me if I think I have a more than 48% chance of losing my phone over the next two years. And while I'm clumsy and forgetful, I've never lost or broken a mobile phone.
So, this policy is a really bad idea for me - I'd do much better to put £6 a month into a savings account and use it to buy something nice at the end of it: maybe a new phone!
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