This math problem is killing me. Anyone explain how it's done?

Question

In nine years, to save up $255,000, how much must be saved back per 3 month period at 3.75% compound interest to meet this goal?

I'm looking at 36x+(.0375x)=255000. But I have this feeling that I'm dead wrong...

I've got a couple answers now, but I can't seem to make them work! I keep getting answers on my calculator like 1.163693418 E -5

I GIVE UP! What's the answer?

Answer 1

When you put things like this into your calculator, use parenthesis -very- generously. This can make a difference between getting an answer in the right ballpark, and getting some nonsense like 1.163693418 E -5
The formulas cited above don't look right,let me look them up and come back to this.
If you have a formula that looks like Amount = Payment x increase factor, you need to solve that formula for payment and get payment = amount / increase factor. Then if you divide amount / number of payments it won't come out right, because the amount itself is compounded. I seem to remember something called a "plan ahead formula" or "savings plan formula" that takes this into account.
When I find the correct formula, if it's not in that form, and if no other answerer has put it into that form, I'll help you with that...
Ok. you can find the formula at
http://www.math.fsu.edu/~blackw/mgf1107fa06/Saving.pdf -
but you still need to solve that formula for D.(the amount of your regular deposits)..
When I solve that formula for D I get
(F(n/r))/((1+(r/n))^(nt) - 1) = D
WIth F = 255000, n = 4, r = .0325, t = 9, plugging this into the calculator, we get
D = $6126.36
This seems like a lot, and it is, because the beauty of compound interest is that you can accumulate a lot of money if you give it plenty of time. 9 years isn't really that long to accumulate this much money at compound interest.
I see you're getting different answers here, that's because the usual compound interest formula assumes a known regular deposit and solves for an amount. But since your principle itself is compounded, solving for the amount isn't just a matter of dividing by the number of deposits. That's why we use the "plan head" formula as cited above.
Now that you haev this formula, you can check it for yourself by solving for D (it's simple algebra), inserting the appropriate numbers, and then entering it -very carefully- into the calculator.
Or you could eliminate all doubt and error, and just go here...
http://www.finaid.org/calculators/savingsplan.phtml

Answer 2

For Quarterly Compounding interest, in a single year, the correct formula is:

Amount = Principle*(1 + r/4)^4

However, you are saving for 9 years, or 36 quarters:

Amount = Principle*(1 + r/4)^36

The question you have to ask is whether the 3.75% is the Annual interest rate, or the quarterly interest rate. If annual, .0375 IS r. If it is the quarterly interest rate (if so, let me know who is paying that rate), then the r/4 IS the .0375.

Let's assume real world: r = .0375

So: 255,000 = P(1 + .0375/4)^36 ==> P = 2.55*10^5/(1 + .0375/4)^36

EDIT - I changed the 3.75 to the proper .0375

This is correct...P = 255000 / 1.399 = $178,688

Answer 3

I'm reading your question as the amount you must save every quarter, not just a one time contribution. The formula is

Amt = Pmt * [ (1+i)^n - 1 ]/i

Where Amt is the amount after n time periods
PMT is the monthly amount
i is the interest rate per time period (if the 3.75% is yearly, you would have to divide it by four to make it quarterly)
n is the number of time periods, in this case, 4 quarters * 9 years or 36

I could derive it for you, but you probably have what you need. If you need the derivation, add a comment to your question.

Answer 4

Say that you're searching x to the -4 power. unfavourable powers mean that the great result's a fragment the position the denominator is the decision if the exponent became effective. right it truly is what I mean: x^-4 = a million/(x^4). So, -2^-6 is a similar as a million/(-2^6). wish that explains it.

Answer 5

A = p((1 + i)^n - 1)/i
assuming quarterly compounding as well as quarterly deposits,
i = 0.0375/4 = 0.009375
p = 255,000(0.009375)/(1 + 0.009375)^27 - 1)
p = $8,343.48