SOLUTION: You currently have $8,800 (Present Value) in an account that has an interest rate of 6% per year compounded daily (365 times per year). You want to withdraw all your money when it

Algebra ->  Equations -> SOLUTION: You currently have $8,800 (Present Value) in an account that has an interest rate of 6% per year compounded daily (365 times per year). You want to withdraw all your money when it       Log On


   

Question 1196114: You currently have $8,800 (Present Value) in an account that has an interest rate of 6% per year compounded daily (365 times per year). You want to withdraw all your money when it reaches $16,720 (Future Value). In how many years will you be able to withdraw all your money?
Answer by ikleyn(52778) About Me  (Show Source):
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You currently have $8,800 (Present Value) in an account that has an interest rate
of 6% per year compounded daily (365 times per year). You want to withdraw all your
money when it reaches $16,720 (Future Value). In how many years will you be able
to withdraw all your money?
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Let "r" be the compound interest rate per annum.

Start from the formula for the future value

    16720 = 8800%2A%281%2B0.06%2F365%29%5En,

where "n" is the number of days.


It is the same as

    16720%2F8800 = 1.000164384%5En,

or

    1.9 = 1.000164384%5En.



Take logarithm base 10 of both sides of the equation

    log(1.9) = n*log(1.000164384).


Find  n = log%28%281.9%29%29%2Flog%28%281.000164384%29%29 = 3904.92 days, or 3905 days, rounded to the closest greater number of days.


3905 days = 10 years 8 months and about 12 days  (counting 365 days/year, 30 days per month).


ANSWER. The time to wait is 3905 days, or 10 years, 8 months and about 12 days.

Solved.