Need Compound interest math help

[mama25angels]

really need some help with this problem, we were able to work the others, but this one is stumping us:

 

Find the amount that savings account of $55,000 would yield at 8% compounded every 3 months over a period of 2 years.

 

 

Thanks

[KAR120C]

really need some help with this problem, we were able to work the others, but this one is stumping us:

 

Find the amount that savings account of $55,000 would yield at 8% compounded every 3 months over a period of 2 years.

 

 

Thanks

If 8% is the nominal rate per year, and it compounds four times a year, then the rate per period is 8%/4... which is 2%... and over two years it would compound 8 times.

 

So you're starting with 55000, and multiplying it by 1.02 (which is like adding 2%) 8 times. As an equation it's 55000(1.02)^8 -- that gets you the ending balance, and you can subtract out the original principal to see what it yielded.

Edited September 16, 2010 by KAR120C
corrected P

[mpcTutor]

really need some help with this problem, we were able to work the others, but this one is stumping us:

 

Find the amount that savings account of $55,000 would yield at 8% compounded every 3 months over a period of 2 years.

 

 

Thanks

 

The previous poster already gave the solution. Here are details.

Simply follow the same logic that you used for other problems solved correctly.

 

If

 

P = Present amount = 55000

 

 

i% = % interest rate per period (Note that I deliberately wrote per period and not per year ) = 8%/4 = 2%

 

 

n = No. of periods for which P is in the saving account = 2 years x 4 period per year = 8

 

 

S = Lump sum amount yielded at the end of n period = To be found

 

 

yield = interest paid on investment

Then

 

S = P( 1 + i%)^n (One can easily derive this formula with 7th grade algebra background. Note 2% = 2 per cent = 2/100 = 0.02))

= 55000 ( 1 + 0.02)^8

 

= 64441.27

 

 

Yield = 64441.27 - 55000 = 9441.27 (Answer)

 

Best regards.

 

mpcTutor

 

http://www.mpclasses.com/ContactUS.htm

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US Central Time:1:49 PM 9/16/2010

[mama25angels]

Thank you so much!!!! We were so close but just couldn't put our fingers quite on it.