Math Problem

[Lucky]

So I you lent someone $1000 in 1978, and it was never paid, what would the amount today likely be with inflation and interest calculated in? Surely there is a math whiz here...? Thanks.

[Guest lurkerspeaks]

So I you lent someone $1000 in 1978, and it was never paid, what would the amount today likely be with inflation and interest calculated in? Surely there is a math whiz here...? Thanks.

not including interest, just calculating inflation, it would be

$3377.65..

here is the "calculator" I used

[Lucky]

Thanks for that, lurkerspeaks. Now can someone tell me the value with interest?

[MsGuy]

A representative inflation rate can be googled up but you will have to specify an interest rate, Lucky.

[TampaYankee]

not including interest, just calculating inflation, it would be

$3377.65..

here is the "calculator" I used

Were interest and inflation figured in the terms of the loan at that time? Few of us could pay off mortgages if we also had to account for inflation over the lifetime of the loan.

I know this is just a math problem and the answer is alot.

Neglecting the effect for inflation, for a fixed interest rate compounded monthly the formula is

Where,

A = final amount

P = principal amount (initial investment)

r = annual nominal interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

For 6% interest compounded monthly from Jan 1 1978 to Jan 1 2011 the total would be $7202 and change, if I plugged in the numbers right.

Straightlining the inflation over the 33 year period yields $198.1666666/yr and changes the compounded amount to $27,708. This underestimates the effect of interest on the inflation amount which grows exponentially, not linearly, over time because the interest grows exponentially. Thus there is an exponential increase in the earned interest amount to be inflated. To make concrete, the 198 inflation added yearly should be 198+ interst on 198 which is then inflated over the the next year and interest on that added to the total and and so forth, compounded for inflation and interest each succeeding year.

The linear assumption is more in line with making a fixed monthly addtion to the principle such as adding a fixed amount monthly to an initial $1000 SRA. But that is a forumla at my finger tips ( http://www.moneychimp.com/calculator/compound_interest_calculator.htm ) so I used it. It gives a lower bound to the amount you seek. I'll let an energetic Einstein chase that refinement.

[Lucky]

In 1978 I bailed a gay guy out of jail from a redneck county. The deputy had told his lawyer that the inmates were after him. So I put up $1000 to buy a $10000 bond. The guy got out and stiffed me for the money. He recently died so I thought I could put a claim on the estate, but the statute of limitations has probably run.

[MsGuy]

$1.000.00 @ 7% compound interest, compounded annually at end of interest period = $9,325.34 in 33 full years. Accruing compound interest is a real beast.

In a real world transaction an anticipated rate of inflation is already discounted into the stated interest rate. 7% is actually a pretty stiff rate of interest for an inflation protected debt.

However, to adjust for inflation, one would simply add in the inflation rate to the stated interest rate. To achieve a reasonably accurate net payoff number, one could google up the CPI (or other desired indicator of inflation) for each year, perform the calculation on this calculator and repeat for 33 iterations.

That's a bit more work than my old brain is up to, so ball parking an approximate inflation rate of 2.5% since 1978 (and using the above assumptions), I come up with a total payoff (@ 9.5%) of $19,983.24.

Adjusting for inflation on top of the stated interest makes a hugh difference. That's why those special inflation protected US bonds carry a much lower rate than the regular US bonds.

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The above calculations act to inflation protect the accuring unpaid interest as well as the principal ($1,000). Another approach would be to adjust the principal for inflation (which would require adding $2,377.65 (per Lurker's calculator) to the $9,325.34 for a total of $11,702.99.

----

And, of course, at 7% simple annual interest (uncompounded), one would have $3,377.65 plus $2,310 ($70/yr. x 33 yrs.) or $5,687.65.

In calculating interest, the devil is in the details. There are actually cuniform records of bankers playing these kinds of games with interest to get around Babylonian restrictions on usury.

[lookin]

Now thas' mah kinda calculatin' !

[MsGuy]

LOL, lookin, I didn't even venture into the wilderness of the rule of 78 or the magical world of prepaid interest.

[TampaYankee]

LOL, lookin, I didn't even venture into the wilderness of the rule of 78 or the magical world of prepaid interest.

Lol... You have impessed me. If I ever encounter you on an auto lot I'll have a firm hand on my wallet.

[MsGuy]

Lol... You have impressed me.

Hahahaha, I once gave a guest lecture on consumer finance at Antioch College (the one in Ohio). About half way through the craziness that is the rule of 78s, I had to segue into a quick Q&A session to finish the lecture. I had not only confused the kids, I had managed to thoroughly confuse myself.

----

Thanks for your post, TY. It reminded me of this lecture and that in turn reminded me of a very close friend of mine who attended Antioch. Tom died 30 odd years ago of MS and I haven't thought of him in a long time. He was one of the smartest, kindest guys I have ever had the honor to call a friend.

----

And for any masochists hanging about, here is an explanation of the Rule of 78s. And if you still don't understand why it's such a racket, well, the friendly guy who finances your next car is gonna love to see you coming though his door.

[Guest NeedSome]

Were interest and inflation figured in the terms of the loan at that time? Few of us could pay off mortgages if we also had to account for inflation over the lifetime of the loan.

I know this is just a math problem and the answer is alot.

Neglecting the effect for inflation, for a fixed interest rate compounded monthly the formula is

Where,

A = final amount

P = principal amount (initial investment)

r = annual nominal interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

For 6% interest compounded monthly from Jan 1 1978 to Jan 1 2011 the total would be $7202 and change, if I plugged in the numbers right.

TY and Ms Guy - you two are SO hot. And I am not being facetious. I know this is really strange, but math really turns me on. Laying in bed in the afterglow and doing some diff eq together...oh dear me if only I could find an escort into that!

[RA1]

I think it very likely you would have much better luck getting an escort to quote Elizabeth Barrett Browning rather than solving a differential equation. However, somewhere out there must be a left brain escort who can accommodate you.

Interesting comment.

Best regards,

RA1

[MsGuy]

In 1978 I bailed a gay guy out of jail from a redneck county. The deputy had told his lawyer that the inmates were after him. So I put up $1000 to buy a $10000 bond. The guy got out and stiffed me for the money. He recently died so I thought I could put a claim on the estate, but the statute of limitations has probably run.

1) You're owed $1,000, no interest or inflation protection accrues unless there's a clear agreement otherwise. Sorry.

2) You're right you have a statute of limitations problem.

3) Depending on how Cali treats claims against an estate, you probably also have a Statute of Frauds problem.

4) Maybe you should have taken it out in trade at the time.

And, finally:

Damn, man, you've got a loooong memory. Remind me never to get on your bad side!