S.O.S. Mathematics CyberBoard

Hi,

Can someone tell me how to re-write this equation in terms of i, thanks.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

There is a mistake in what you have written. No matter how I put in parentheses this is impossible as written.

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It should be correct. I have simplified a bit. But the equation is correct. Perhaps seeing the question will clarify the equation I wrote.

Matt inherited as a trust of a fifteen-year annuity-immediate with annual payments. He has been told that the
annuity payments earn compound interest at a level rate and that at the end of fifteen years, their accumulated
value will be $37,804.39. He has further been assured that figured at this same rate of interest, the value of his
inheritance was $15,077.10. The trust executor will not reveal the amount of annual payments. Determine this
amount and also the annual effective interest rate earned by the annuity payments.

(1+i)^15 - 1 / 1 - (1+i)^15 = 37804.39/15077.10

The equation of s angle n is [(1+i)^n]/i.

and the equation of a angle n is [1-(1+i)^n]/i. The i's cancel out to give you the above equation. Please let me know if that is not right.

The equation cannot be right, first of all--as written, the left-hand side is just -1, and we can all agree -1 is not equal to 37804.39/15077.1 as the latter is positive.

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Agree with Shadow; your equations are wrongly shown:
didn't check but I think due to lack of proper bracketing...

Anyway, here's how I'd attack your problem:

Step#1: determine the rate:
15077.10(1 + i)^15 = 37804.39
i = (37804.39 / 15077.10)^(1/15) - 1 ; .0632 or 6.32%

Now you're left with calculating the annual payment;
same as a loan of 15077.10 over 15 years at annual interest = 6.32%.
Formula:
P = Ai / [1 - (1+i)^(-n)]
where:
P = Payment (?)
A = Amount borrowed (15077.10)
n = number of payments (15)
i = interest (.0632)

P = 15077.10 * .0632 / [1 - 1.0632^(-15)] = 1585.00

Surprisingly no cents in the payment!

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Maybe, but I couldn't figure out a bracketing where it actually worked, parentheses the first two terms, or both pairs and you still get -1 on the LHS. It would be less highly trivial if it were just the last two terms, I suppose, then you have which at least could be solved.

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This is what the "account" will look like:

It is same as a loan: the Bank is theoretically borrowing from you
and paying you back in annual payments: capish?

Equation (once more!):
P = Ai / [1 - (1+i)^(-n)] where i = (37804.39 / A)^(1/n) - 1

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