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Tue 20 Mar, 2007 12:19 pm
Please help me with what is a sequence problem:
Consider an investment of $200 000, annual interest rate 14% compounded monthly, with monthly payments of $8 000. Estimate how long it takes for the initial investment to double in value. Does it take the same time to double again?
This question is from my programming course, but to program this I will need to know the algebra. I could just look at the graph I can compute from the information, but I do not know if this is what is wanted, or a progam needs to be written to solve it.
Anyway, if 'I' is the initial investment, p the payment and i the monthly interest rate, then the first term of this sequence is:
I
The second:
I + (I + p)*i
(If we let the second term = k)Third:
k + (k +p)*i
and so on, simplifying gives the sequence:
I; I(1 + i) + pi; I(1 + i)^2 + 2pi(1 + i); I(1 + i)^3 + pi(2i(1 + i)+1);...
How do we get the general term? Obviously it is something like
I*(1 + i)^(n - 1) + ...
but what about the part with p? Help is much appreciated, thanks.
I figured this using Excel, the totals on the right are figured after the month is over. This also assumes the 8000 is not included with the initial investment.
Month Balance
1........ 228,000
2........ 269,040
3........ 315,826
4........ 369,161
5........ 429,964
6........ 499,279
7........ 578,298
8........ 668,379
9........ 771,072
10...... 888,143
My formula takes the total from the previous month, adds 8000, then multiplies that by 1.14. X=(X+8000)*1.14
You may want to change your lower case i to R (rate) so you don't have two I's in your equation. I don't see that k is even necessary.
T
Yes, i can get the numerical sequence, but how do i get the general term?
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