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.