Interest rate problem: at what interest rate will ....

[Guest]

Does anyone know how to set this interest problem up::

At what percent interest rate will $600 grow to $850 if invested for 4.8 years and interest is compounded quarterly?

Thanks !

 

[stapel]

Just plug into the compound-interest formula you memorized: A = P(1 + r/n)^nt, with P = 600, A = 850, t = 4.8, and n = 4. Solve for the rate r.

Eliz.

 

[Guest]

did you get the rate to be .053? I wasn't positive on how to do this.

 

[tkhunny]

Well, let's see...

\(\displaystyle 600*(1+\frac{0.053}{4})^{4.8*4}=772.521\)

Nope. That's not it. If you had shown your work, I may have been able to tell you where you wandered off.

 

[Guest]

I set it up as : 850=600(1+x/4)^(4.8 * 4)
I multiplied the exponents, and got 33.6. Then I cancelled them out by multiplying them by 1/33.6
I divided by 600 on both sides and got (17/12)^ (1/33.6) = 1+(x/4)
then, to get rid of the 4 in the denominator, I multiplied by 4/1 on both sides and came up with
(68/12)^(1/33.6)=1/x
I raised 68/12 to the exponents, and then subtracted 1 to ge x=.053

 

[skeeter]

850 = 600(1 + x/4)^4.8*4

4.8*4 = 19.2 ... where did you get 33.6?

850 = 600(1 + x/4)^19.2

divide both sides by 600 before dealing with the exponents ...

17/12 = (1 + x/4)^19.2

(17/12)^1/19.2 = 1 + x/4

(17/12)^1/19.2 - 1 = x/4

4[(17/12)^1/19.2 - 1] = x

.073 = x

 

[Denis]

Does anyone know how to set this interest problem up::

At what percent interest rate will $600 grow to $850 if invested for 4.8 years and interest is compounded quarterly?

Thanks !

Are you sure of the 4.8 years Amanda?
Could it be 4.75 years (since compounding is quarterly) ?