Question

Please Help !!!!!!

How long (in years) would it take $9,900 to grow into $22,800 if it's compounded continuously at 4% interest per year?

Answer= ____ years (Round your answer to 2 decimal places.)

Answer 1

21.27 years

Explanation:

22800 = 9900(1.04^t)

22800/9900 = 1.04^t

76/33 = 1.04^t

ln(76/33) = t×ln(1.04)

t = 21.27

Answer 2

Answer: it will take 20.83 years.

Explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 9900

A = 22800

r = 4% = 4/100 = 0.04

Therefore,

22800 = 9900 x 2.7183^(0.04 x t)

22800/9900 = 2.7183^0.04t

2.3 = 2.7183^0.04t

Taking ln of both sides, it becomes

Ln 2.3 = 0.04t ln2.7183

0.833 = 0.04t

t = 0.833/0.04

t = 20.83 years