Question

if you have $1,490 today, how much will it be worth in six years at 9 percent per year compounded continuously? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The future value of $1,490 compounded continuously at a 9% annual interest rate for six years is $2,556.82.

Step-by-step explanation:

The question involves calculating the future value of an investment using the formula for continuous compounding. The formula is F = Pert, where P is the principal amount (the initial amount of money), r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the base of the natural logarithm, approximately equal to 2.71828. For the given problem:

P = $1,490

r = 0.09 (9% expressed as a decimal)

t = 6 years

Inserting these values into the formula gives us:

F = $1,490 * e(0.09*6)

Calculating this yields the future value:

F = $1,490 * e0.54

F = $1,490 * 1.716007 (calculated using a calculator with the ex function)

F = $2,556.82 (after rounding to two decimal places)

Therefore, $1,490 today will be worth $2,556.82 in six years at a 9 percent annual interest rate compounded continuously.