Compond Interest

Question

Find the present value of $126,488.02 due in 9 years at an interest rate of 11%/year compounded continuously. 

Answer 1

The base of the natural logarithm e is taken as 2.718281828.

Here construct the equation $126488.02 = Pe^(0.11x9)

which puts P (for Present Value or Principal) at

$46999.99993 (or $47000.00).

For continuous compounding of an amount at an annual

interest rate of r percent, one considers the amount to be 

compounded a huge number of times per year such as

1000000000 (or one billion) times.

This follows from the proven equality of e^x

to the limit_{[as n goes to positive infinity]}

of {1 + x/n}ⁿ.

This is confirmed by calculating 46999.99993 times e^0.99 and then by 

evaluating 46999.99993 times (1 + 0.99/10⁹)^1000000000. Both results

come to 126488.02.