Walter B. answered • 04/28/17

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This is a future value problem where we are solving for the number of compounding periods.

The future value formula is:

Future Value = Present Value * (1 + per period interest rate)^(number of compounding periods)

Per period interest rate = annual percentage rate/# of annual periods

Per period interest rate = .06/365 = .00016438356

1000 = 100* (1.00016438356)^(number of compounding periods)

Dividing both sides by 100 yields

1000/100 = (1.00016438356)^(number of compounding periods)

in order to solve for the number of compounding periods, we take the natural logarithm of both sides and note that a^b is b*logarithm a

ln (10) = ln((1.00016438356)^(number of compounding periods)) = (number of compounding periods) *

ln(1.00016438356)

divide both sides by ln(1.00016438356)

ln (10)/ln(1.00016438356) = number of compounding periods = 14008.5439 days

To convert back to years, divide by 365 14008.5439 days/365 days per year = 38.380 years