Compound Interest

[Dan9902]

Could someone explain to me how these are done I cant figure out how to properly use these formulas. Thank you

Suppose an investment of $9725.38 is held for 8 quarters at a rate of 3.36% compounded quarterly,
what will be the value of the investment at maturity?

An investment grows from $12706.55 to $15330.39 at a rate of interest of 3.91% per year compounded biweekly.
How many years was the investment held?

 

[Steven G]

Which formula are you trying to use and why are you having trouble properly using the formulas?

 

[Dan9902]

Which formula are you trying to use and why are you having trouble properly using the formulas?

Which formula are you trying to use and why are you having trouble properly using the formulas?

The first one I am not understanding. The second one I am using (FV/PV) / (1+0.0391/26). Its giving me small decimal answers which doesn't work.

 

[tkhunny]

#1 Why do you need a formula for anything? Why not just consider the structure and write it down?

Yrs = 2 -- (8 quarters)

[math]9725.38 \cdot\left(1 + \dfrac{0.0336}{4}\right)^{4\cdot Yrs} = [/math]
#2 Small wonder the formula doesn't work. It's missing pieces. That's why making sense of it without trying to use some artificial memorization is so important.

Yrs is the number of years.

[math]12706.55\cdot\left(1+\dfrac{0.0392}{26}\right)^{26\cdot Yrs} = 15330.39[/math]
Use your best algebra to find Yrs.

 

[Dan9902]

#1 Why do you need a formula for anything? Why not just consider the structure and write it down?

Yrs = 2 -- (8 quarters)

[math]9725.38 \cdot\left(1 + \dfrac{0.0336}{4}\right)^{4\cdot Yrs} = [/math]
#2 Small wonder the formula doesn't work. It's missing pieces. That's why making sense of it without trying to use some artificial memorization is so important.

Yrs is the number of years.

[math]12706.55\cdot\left(1+\dfrac{0.0392}{26}\right)^{26\cdot Yrs} = 15330.39[/math]
Use your best algebra to find Yrs.

Thank you now I kind of understand, I ended up figuring out the second one on my own lol I realized I was missing the In
but for an example like this. Pedro made an investment at the beginning of January, 2000. It has grown to be $54550.07 by the beginning of April, 2006. At a rate of interest of 6.71% per year compounded monthly, what was the initial investment?

I tried setting it up like this $54550.07/1+0.0671/12)^12*6.3 I got it wrong I was a few decimal points behind could you explain why I got it wrong please?

 

[Otis]

… 54550.07/1+0.0671/12)^12*6.3 … [my answer] was [off a bit] … could you explain …

Hi Dan. I'm not sure what you did, but I'd guess your answer is off because you rounded (6+1/4) years up to (6+3/10) years.

\[\frac{54550.07}{\bigg (1 + \dfrac{0.0671}{12} \bigg)^{12\;·\;6.25}}\]

That expression equals $35,906.28 -- we type it as shown below. Grouping symbols are required around (bases)^(exponents) that contain more than one number or symbol, and the same goes for [denominators].

54550.07/[(1 + 0.0671/12)^(12*6.25)]

If your incorrect answer is not $35,786.35, then something additional happened.

?