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Math Help - Compounded Interest











































A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?

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May 06, 2011
Compound Interest Calculation
by: Staff

The question:

A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?


The answer:

The interest rate paid by the bank is a constant: 5% per year.

The function which describes a constant % rate of change is called an exponential function.

It has the form:

f(t) = (initial value)*(1 + rate of change)^t


------------------------------------------------------------
Definitions:

t = time in years

(1 + rate of change) is called the "growth factor" if its value is greater than 1.

(1 + rate of change) is called the "decay factor" if its value is less than 1, but greater than 0.


(1 + rate of change)^t = (1 + rate of change) raised to the "t" power

------------------------------------------------------------


For your problem, different variable names are generally used, but the equation is the same

f(t) = (initial value)*(1 + rate of change)^t

A = P*(1 + r)^t

A = final balance in the savings account
P = principle (the initial deposit in the bank)
r = decimal form of annual interest rate
t = time in years

P = $500
r = .05 (this is the decimal form of 5%. It is = 5%÷100)
t = 10 years


A = P*(1 + r)^t

A = $500*(1 + .05)^10

A = $500*(1.05)^10

A = $500*(1.62889463)

A = $814.447313

A = $814.45 (rounded to the nearest penny)

The final answer is: A = $814.45





Thanks for writing.


Staff
www.solving-math-problems.com


Jul 24, 2011
LOST
by: Anonymous

I was really struggling with this and needed to see the steps. I have one more question could anyone tell me where the number (1.62889463) came from ? I understood the rest thanks so much !


Jul 24, 2011
Compounded Interest Factor
by: Staff


The answer:

(1.05)^10 = (1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)*(1.05)


(1.05)^10 = 1.62889463


You should use a calculator which will compute an exponential function or a good interest rate table to verify this value.



Here is a link to a downloadable interest rate table:

http://www.oup.com/us/pdf/eeconstuds/interestTables.pdf


Go to page 15 – it will say 5% at the top of the page:

Look at the very first column on the left hand side of the page. It is labeled “n”.

Read down the column to n=10

Look at the number listed in the adjacent column.

The number listed is: 1.629 (a rounded version of 1.62889463)




Thanks for writing.

Staff
www.solving-math-problems.com

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