I've been out of my College Algebra class for two weeks with mono, strep, and jaundice (oh boy!). I've never well understood compound interest, but I think I get it from teaching myself. I'm trying to get a headstart on making up my work, and the paper asks:
What is the interest rate of an account that doubles your money in seven yeas when interest is compunded quarterly?
My answer is some horrible thing. I'll describe it:
4(Twenty-eighth root of the principal)-4=r
Is this correct? Would anyone like to confirm this or help me?
Thanks.
>>1
OK, first recognize the compound interest equation:
A=A0(1 + i)n where A0 is the amount of money at the start (time zero), A is the amount you have after time t years, i is the interest rate per compounding period (take the given nominal rate and divide it by the compounding frequency, 4 for quarterly), and n is the total number of compounding periods (equal to the compounding frequency 4 times the total time in years).
Name:
Anonymous2010-10-02 1:30
Next, recognize the compound interest equation rearranged to solve for i:
i = nthROOT(A/A0) - 1
Nominal (i.e. annually expressed) rate j = 4i compounded quarterly, so we have i = j/4 and:
j/4 = nthROOT(A/A0) - 1, and so:
j = 4(nthROOT(A/A0) - 1)
Name:
Anonymous2010-10-02 1:36
Substituting the specifics about 7 years and doubling your money, the value of n must be 7 times 4 or 28 compounding periods, and the value of (A/A0) must be 2 (if your money has doubled, then the money you end up with divided by the money you started with must be 2). We have:
j = 4(28thROOT(2) - 1)
So, you had a single error where you put principal where simply the number 2 belongs. The actual principal is not important to the solution.
Name:
Anonymous2010-10-02 1:43
The value of j rounded to four decimal places calculates to 0.1003, so we have about 10.03% compounded quarterly will double your money, regardless of principal, in 7 years.