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.
To find the annual amount of money that must be deposited in order to save $110,000 in 9 years with a 10% interest rate 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 amount (the annual deposit we need to find)
e = the mathematical constant approximately equal to 2.71828
r = the interest rate as a decimal (10% = 0.10)
t = the time period in years (9 years)
Rearranging the formula, we have:
P = A / e^(rt)
Now, let's plug in the values:
P = $110,000 / e^(0.10 * 9)
To calculate e to the power of (0.10 * 9), we can use a scientific calculator or an online calculator. Once you calculate this value, divide $110,000 by the result to find the annual amount that must be deposited each year.
Please note that the value of e to the power of (0.10 * 9) is approximately 1.999 and rounding it to the nearest cent would give us $55,077.01. Therefore, the annual amount of money that parents must deposit each year to save $110,000 in 9 years for a child's college expenses is approximately $55,077.01.