A bank account earns 10 percent interest compounded continously. What annual amount of money must parents deposit each year in order to save 110000 dollars in 9 years for a child's college expenses? Assume the annual amount is added continuously over the period of each year.
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To find the annual amount of money that parents must deposit each year to save $110,000 in 9 years with 10 percent interest compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount (in this case, $110,000)
P = the principal (the annual deposit)
e = Euler's number, approximately 2.71828
r = the interest rate (in decimal form, 0.10)
t = the time period (in this case, 9 years)
First, let's rearrange the formula to solve for P:
P = A / (e^(rt))
Now, substitute the given values into the formula:
P = 110000 / (2.71828^(0.10*9))
To solve this equation, we will need to use a calculator that has an exponential function (usually denoted by "e^x").
P = 110000 / (2.71828^0.9)
P ≈ 110000 / 2.4596
P ≈ 44709.40
Therefore, the parents must deposit approximately $44,709.40 each year to save $110,000 in 9 years for their child's college expenses.