Help with variable in denominator, within ( ) and with exponent

[aereperennius]

Hi.

I'm a finance student, and I've spent the last two years taking economics, accounting, and general business stuff. It's been two years since taking a math class, and now that the finance classes are finally getting hard, I cannot remember how to do the basic algebra!

I have a problem that starts as 92.70=102.5/(1+x/2)^4.

I multiplied both sides by the denominator on the right to get 92.70(1+x/2)^4=102.5

Then I divided by 92.7 to get (1+x/2)^4=1.11

However, at this point, I'm totally stuck. Any help is greatly appreciated!

 

[Ishuda]

Hi.

I'm a finance student, and I've spent the last two years taking economics, accounting, and general business stuff. It's been two years since taking a math class, and now that the finance classes are finally getting hard, I cannot remember how to do the basic algebra!

I have a problem that starts as 92.70=102.5/(1+x/2)^4.

I multiplied both sides by the denominator on the right to get 92.70(1+x/2)^4=102.5

Then I divided by 92.7 to get (1+x/2)^4=1.11

However, at this point, I'm totally stuck. Any help is greatly appreciated!

You now need to take the 4th root of both sides
((1+x/2)⁴)^(1/4) = 1 + x/2 = 1.11^1/4
or
x = 2 (1.11^1/4 - 1) = 0.05

 

[aereperennius]

I got it now. Thank you!!!

 

[lookagain]

In case you're interested, your problem was
calculating the present value of $102.50 <-------
at a rate of 5% annual cpd semiannually,
for 2 years....agree, Ishuda?

It doesn't check correctly to the nearest cent. It's off by 32 cents, because the interest rate has
been rounded to two decimal places of 0.05, instead of to at least the four decimal places of 0.0509
needed.


\(\displaystyle \$92.70\bigg(1 \ + \ \dfrac{0.05}{2}\bigg)^{2*2} \ =\)


\(\displaystyle \$92.70(1.025)^4 \ \approx \)


\(\displaystyle \$102.32\)

 

[Ishuda]

In case you're interested, your problem was
calculating the present value of $102.50
at a rate of 5% annual cpd semiannually,
for 2 years....agree, Ishuda?

Sounds very reasonable to me although one might quibble over a few pennies because of round off errors [as I am likely to do sometimes]. Actually, since the money is rounded off semi-annually, the value at the end of two years would be $102.34.