Amidst all the other current economic woes, the pound has been falling and the high street commercial rate is now below parity. I must check to see if I have any Euro notes lying around...
And the old debate about whether or not to join the Euro is slowly coming to the forefront, although the levels of political ferocity seen in the past haven't yet materialised. But one point I haven't seen much of is the debate over which interest rate is better for this country - the Bank of England's 2% or the European Central Bank's 3%?
A single percentage point doesn't look that much different, does it? Yet such a difference has very real consequences for borrowers and savers, for mortgage levels, for taxation - one cold go on endlessly. Not for nothing does the Bank of England's Monetary Policy Committee decisions get heavily analysed, even when the rate is shifted only 0.25%.
So is anyone calling for the UK to have the ECB interest rate? Because that is what entering the Euro will involve. The British economy has long followed a different path from that of many other European countries and frequently the two interest rates have moved in opposite directions because of this. Joining the Euro is not going to change all this. Nor is it going to be a magical solution to current economic problems.
Showing posts with label interest rates. Show all posts
Showing posts with label interest rates. Show all posts
Sunday, December 14, 2008
Friday, December 12, 2008
More thoughts on interest rates
Further to my post Very long term interest rates I've been giving the subject some more thought, not for the sake of time travellers but as a possible means by which a pension fund might be created.
Now just imagine that if when a person is born, a long-term saver account were set up that could not have a withdrawal for 65 years. Imagine that £1000 were deposited in it. How much would there be for the person when they retire?
If we take the 5% interest rate then we get £23,839.90. Hmm... it's not really that high an amount for several years is it? What about 8%? £148,779.85. How about 10%? Admittedly it's a high rate but we are talking about extremely low liquidity. We get £490,370.73 - now this is more like it. But we have the curse of inflation still.
What about an alternative model of keeping the rate at 5% but adding £100 to the account each year? We get £69,519.70. On 8% we get £333,504.65. 10% produces £979,741.45 (but once again waiting just one extra year brings the ~illionaire status).
And if we take a 5% interest rate but tie the additional deposit to rise at an inflation rate of 2%? We get £92,578.98. On an 8% rate we get £395,547.30.
So is there anything in this model that could be a workable solution for pensions? The biggest problems are still relying on the interest rate being high enough (even if it's the average of a variable rate) - and on the adding model it really needs to at least 7% for the resulting amount to be even vaguely reasonable at today's prices - and inflation. If we follow historians of the 1930s who use multiplying by 30 as their method of giving very rough modern day equivalents, then on an 8% rate with a yearly additional £100 inflated by 2% per annum we find a 65 year fund yields the rather low equivalent lump sum of £13,184.91.
(For those still thinking about the Monk's 200 year plan from the last post, we might try a 100* method. On an 8% rate with no additions he'd get the equivalent of £48,389,495.85.)
A 12.5% rate seems somewhat high, even so for such a non-liquid account, but would yield the equivalent of £138,741.61. If you could then maintain that interest rate for a simple interest payout, you'd then get an annual pension equivalent to £17,342.70. But there's a huge amount of "if"s in there and viability can't be ensured. This doesn't seem like a long-term solution to pensions.
Now just imagine that if when a person is born, a long-term saver account were set up that could not have a withdrawal for 65 years. Imagine that £1000 were deposited in it. How much would there be for the person when they retire?
If we take the 5% interest rate then we get £23,839.90. Hmm... it's not really that high an amount for several years is it? What about 8%? £148,779.85. How about 10%? Admittedly it's a high rate but we are talking about extremely low liquidity. We get £490,370.73 - now this is more like it. But we have the curse of inflation still.
What about an alternative model of keeping the rate at 5% but adding £100 to the account each year? We get £69,519.70. On 8% we get £333,504.65. 10% produces £979,741.45 (but once again waiting just one extra year brings the ~illionaire status).
And if we take a 5% interest rate but tie the additional deposit to rise at an inflation rate of 2%? We get £92,578.98. On an 8% rate we get £395,547.30.
So is there anything in this model that could be a workable solution for pensions? The biggest problems are still relying on the interest rate being high enough (even if it's the average of a variable rate) - and on the adding model it really needs to at least 7% for the resulting amount to be even vaguely reasonable at today's prices - and inflation. If we follow historians of the 1930s who use multiplying by 30 as their method of giving very rough modern day equivalents, then on an 8% rate with a yearly additional £100 inflated by 2% per annum we find a 65 year fund yields the rather low equivalent lump sum of £13,184.91.
(For those still thinking about the Monk's 200 year plan from the last post, we might try a 100* method. On an 8% rate with no additions he'd get the equivalent of £48,389,495.85.)
A 12.5% rate seems somewhat high, even so for such a non-liquid account, but would yield the equivalent of £138,741.61. If you could then maintain that interest rate for a simple interest payout, you'd then get an annual pension equivalent to £17,342.70. But there's a huge amount of "if"s in there and viability can't be ensured. This doesn't seem like a long-term solution to pensions.
Tuesday, December 09, 2008
Very long term interest rates
All the recent interest rate cuts have got me thinking about a few situations in various science fiction series where characters can take advantage of (or suffer from) very long term compound interest. Some of these are worth a little thought as to whether such a situation could truly work.
The first one is the Doctor Who story The Time Meddler in which it's revealed, amongst other things, that one of the Monk's previous schemes involved depositing £200 into a London bank in 1968 then nipping forward in time 200 years and collecting a fortune in compound interest. Just how possible might this scheme be? (For the moment we'll ignore the fact that in the Doctor Who universe 2168 is around the end of The Dalek Invasion of Earth which might have caused some disruption to the banking system.)
Now let's start by assuming that either the interest rate remains approximately the same or the Monk was able to get a fixed rate long term account, though that's a big if. Otherwise the scheme could have been derailed by the bank rapidly passing on cuts in interest rates to savers, but not passing on rises so hurriedly. Let's also assume the Monk chose a bank that he knew would be in operation in 200 years time. Whilst there are protection mechanisms for savers if the bank goes under, it's better to use one with the least fuss.
So assuming a fixed rate of 5% (historically the usual interest rate) across the entire period, then exactly 200 years would yield £3,458,516.16 If the interest rate was higher, say 8%, then the outcome rockets to £967,789,916.98 (though if he waited another year he'd be a billionaire). And if he could find a bank insane enough to offer him a fixed interest rate as high as 18% then he'd get £47,580,769,007,364,000.00 Not bad eh?
But there are two fairly major problems. The first is that the Monk would have to somehow be able to claim the account after 200 years' dormancy. He could, I suppose, pose as the descendant of the original depositor, but might run into problems with inheritance tax. Or he could open in the account by posing as a father wishing to create a nest egg for a newly born son, then nip forward in stages and by posing as each successive generation he could transfer the account down. Or he could claim he was an eccentric who wished to help his descendants and make an arrangement for the account to only become active upon the rightful heir claiming it. He could, of course, use an overseas bank in a country that will never have the inheritance tax. The other problem also relates to the tax on interest, though again the Monk could use an overseas bank. A time traveller could be expected to know what they were up to.
And one final problem is inflation. Any major hyperinflation would wipe out the value of the savings. Even normal inflation will reduce it, but so long as the interest rate could keep ahead of that it wouldn't be so much of a problem.
A more interesting case comes in the Red Dwarf episode "Me²". In one scene Holly tells Lister the following:
Given that Lister is hardly the most organised of people, I'm going to assume his bank account is just a current account with an anaemic rate of interest - let's say 0.1%. (And I'm also going to assume that the bank calculates the exact interest rather than rounding it to the nearest whole, which is significant for the first few milleniums.) So even after 300 years Lister would have only £23.62 on deposit. After 3000 years it is £350.97. But after 30,000 years it has risen to £184,230,880,712,550.00. And after 3,000,000 years it has risen to £2.9886565148476356806364059915386 x 10 to the power of 1303. That's a very big number.
And this is where the whole thing would get messy. Interest doesn't grow like a tree, it is made by banks taking their depositors' money and investing it, then giving them a return. And current accounts have terms and conditions that allow the depositor to withdraw the lot instantly, so a bank would be vulnerable to a run if it didn't have reasonable funds available. At some point there just wouldn't be any more money that a bank could make and the interest payments would grind to a halt. The anaemic interest rate would, however, mean that the bank wouldn't have that much to make proportionally, but it would still be tricky. They could, I suppose, offer to buy Lister out of the account with a fixed amount and get a court order or special legislation to impose it upon him if he can't be reached, but that might have side effects on consumer confidence. Equally they could, I suppose, take a risk on Lister not returning and use his money to run the economy, but it would be a big risk. But then the entire scene is a joke being played on someone not au fait with all this.
Another jokey one is in The Hitchhiker's Guide to the Galaxy where we learn about how to pay for a meal at the Restaurant at the End of the Universe, located at the end of time which is 576,000,003,579 years away, as counted by Marvin. This is an underestimate according to Wikipedia: Future of an expanding universe will be about 10 to the power of 10 the power of 76 years in the future. My computer's calculator cannot even process that number. For the meal you just deposit one penny into your bank account and then by the end of the universe compound interest will pay for the bill. The computer still can't calculate even 576,000,003,579 years' worth of interest at 0.1% so we'll just have to assume it's a big amount. Again we have to wonder how the banks can manage it, but the whole thing is impossible, but then so is the entire basis of the Restaurant.
Sadly time travel and stasis are not yet available and so we're all mortals on a rather shorter scale. And current interest rates are so low that if you can find a long term account with a fixed rate good enough to grow a fortune for your great, great, great grandchildren then you're very lucky and they will be luckier still.
The first one is the Doctor Who story The Time Meddler in which it's revealed, amongst other things, that one of the Monk's previous schemes involved depositing £200 into a London bank in 1968 then nipping forward in time 200 years and collecting a fortune in compound interest. Just how possible might this scheme be? (For the moment we'll ignore the fact that in the Doctor Who universe 2168 is around the end of The Dalek Invasion of Earth which might have caused some disruption to the banking system.)
Now let's start by assuming that either the interest rate remains approximately the same or the Monk was able to get a fixed rate long term account, though that's a big if. Otherwise the scheme could have been derailed by the bank rapidly passing on cuts in interest rates to savers, but not passing on rises so hurriedly. Let's also assume the Monk chose a bank that he knew would be in operation in 200 years time. Whilst there are protection mechanisms for savers if the bank goes under, it's better to use one with the least fuss.
So assuming a fixed rate of 5% (historically the usual interest rate) across the entire period, then exactly 200 years would yield £3,458,516.16 If the interest rate was higher, say 8%, then the outcome rockets to £967,789,916.98 (though if he waited another year he'd be a billionaire). And if he could find a bank insane enough to offer him a fixed interest rate as high as 18% then he'd get £47,580,769,007,364,000.00 Not bad eh?
But there are two fairly major problems. The first is that the Monk would have to somehow be able to claim the account after 200 years' dormancy. He could, I suppose, pose as the descendant of the original depositor, but might run into problems with inheritance tax. Or he could open in the account by posing as a father wishing to create a nest egg for a newly born son, then nip forward in stages and by posing as each successive generation he could transfer the account down. Or he could claim he was an eccentric who wished to help his descendants and make an arrangement for the account to only become active upon the rightful heir claiming it. He could, of course, use an overseas bank in a country that will never have the inheritance tax. The other problem also relates to the tax on interest, though again the Monk could use an overseas bank. A time traveller could be expected to know what they were up to.
And one final problem is inflation. Any major hyperinflation would wipe out the value of the savings. Even normal inflation will reduce it, but so long as the interest rate could keep ahead of that it wouldn't be so much of a problem.
A more interesting case comes in the Red Dwarf episode "Me²". In one scene Holly tells Lister the following:
"It seems when you left Earth three million years ago... you left seventeen pounds, fifty pence in a bank account. Thanks to compound interest you now own ninety-eight percent of all the world's wealth, but since you've hoarded it for three million years nobody's got any money except for you and NorWEB."Now this scene is a wind-up in a comedy series, but the basic principles are still present. This time round we would have to assume that a person who is frozen in stasis (basically suspended animation) for a very long time can resume their financial affairs upon being released, which makes sense, although three million years is stretching it. If we can accept that the human civilisation (or its successor) still exists after three million years and a person's bank account can remain active then what does this yield?
Given that Lister is hardly the most organised of people, I'm going to assume his bank account is just a current account with an anaemic rate of interest - let's say 0.1%. (And I'm also going to assume that the bank calculates the exact interest rather than rounding it to the nearest whole, which is significant for the first few milleniums.) So even after 300 years Lister would have only £23.62 on deposit. After 3000 years it is £350.97. But after 30,000 years it has risen to £184,230,880,712,550.00. And after 3,000,000 years it has risen to £2.9886565148476356806364059915386 x 10 to the power of 1303. That's a very big number.
And this is where the whole thing would get messy. Interest doesn't grow like a tree, it is made by banks taking their depositors' money and investing it, then giving them a return. And current accounts have terms and conditions that allow the depositor to withdraw the lot instantly, so a bank would be vulnerable to a run if it didn't have reasonable funds available. At some point there just wouldn't be any more money that a bank could make and the interest payments would grind to a halt. The anaemic interest rate would, however, mean that the bank wouldn't have that much to make proportionally, but it would still be tricky. They could, I suppose, offer to buy Lister out of the account with a fixed amount and get a court order or special legislation to impose it upon him if he can't be reached, but that might have side effects on consumer confidence. Equally they could, I suppose, take a risk on Lister not returning and use his money to run the economy, but it would be a big risk. But then the entire scene is a joke being played on someone not au fait with all this.
Another jokey one is in The Hitchhiker's Guide to the Galaxy where we learn about how to pay for a meal at the Restaurant at the End of the Universe, located at the end of time which is 576,000,003,579 years away, as counted by Marvin. This is an underestimate according to Wikipedia: Future of an expanding universe will be about 10 to the power of 10 the power of 76 years in the future. My computer's calculator cannot even process that number. For the meal you just deposit one penny into your bank account and then by the end of the universe compound interest will pay for the bill. The computer still can't calculate even 576,000,003,579 years' worth of interest at 0.1% so we'll just have to assume it's a big amount. Again we have to wonder how the banks can manage it, but the whole thing is impossible, but then so is the entire basis of the Restaurant.
Sadly time travel and stasis are not yet available and so we're all mortals on a rather shorter scale. And current interest rates are so low that if you can find a long term account with a fixed rate good enough to grow a fortune for your great, great, great grandchildren then you're very lucky and they will be luckier still.
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