# 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?

### Comments for Math Help - Compounded Interest

 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 samef(t) = (initial value)*(1 + rate of change)^tA = P*(1 + r)^tA = final balance in the savings accountP = principle (the initial deposit in the bank)r = decimal form of annual interest ratet = time in yearsP = \$500r = .05 (this is the decimal form of 5%. It is = 5%÷100)t = 10 yearsA = P*(1 + r)^tA = \$500*(1 + .05)^10A = \$500*(1.05)^10A = \$500*(1.62889463)A = \$814.447313A = \$814.45 (rounded to the nearest penny)The final answer is: A = \$814.45Thanks 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