# FINANCIAL MATH: Question on Compounding Interest Semi-annually

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!

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

$$\ln 5 = \ln 1.0325^{2n}$$

By a property of logarithims,

$$\ln 5 = 2n \cdot \ln 1.0325$$

I think you can handle it from here :)

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