FINANCIAL MATH: Question on Compounding Interest Semi-annually

[nicole]

HELP! i know this is an easy question to solve but i need some help. THANKS for any help in advance!

QUESTION: Determine, to the nearest half year, how long it will take $100 to amount to $500 at 6 1/2% compounded semi-annually.

Using the formula A=P(1 + i)*to the power of*n
where A is the final amount, P is the present value, i is the interest rate and n is the number of compounding periods i have gotten to:
A=$500 P=$100 i=6.5%/2 (because it's semi-annually)=3.25% n=2 x n (because it's semi-annually)
In the FORMULA"
A = P(1+i)*to the power of*n
500 = 100(1+0.0325)*to the power of*2n
5 = 1.0325*to the power of*2n
*I am sure the answer is right to this point, I'm just not sure of how to solve for the exponent 2n. thank you for any help!

 

[relinquished™]

Hello Nicole,

In financial mathematics, the best method in solving for unknown time is by the use logarithms, preferably, the natural logarithm \ln.

So far, you're solution is right.

From 5 = 1.0325^{2n}, apply the natural log to both sides

<br /> \ln 5 = \ln 1.0325^{2n}<br />


By a property of logarithims,

<br /> \ln 5 = 2n \cdot \ln 1.0325<br />

I think you can handle it from here :)

 

[Jameson]

A(t) = P(1 + \frac{r}{n})^{(n)(t)}