If P dollars is deposited in a savings account that pays interest at a rate of r % per year compounded continuously, find the balance after t years. (Round your answer to the nearest cent.)

P = 100, r = 2 1/2, t = 12

Answer: $135

Step-by-step explanation:

Continuously compounded interest is calculated as A = Pe^ (rt)

Where:

P is the Principal, given as 100

r is the interest rate, given as 2 1/2 = 2.5% = 2.5/100 = 0.025

t is the time given as 12

e is a constant approximated as 2.7183.

Slot in the given values into the formula:

A = 100 x 2.7183^ (0.025 x 12)

A = 100 x 2.7183^ (0.3)

A = 100 x 1.3498

= $134.986

Approximated to the nearest cent = $135 as the fractional part is greater than 0.5, therefore, we round up to the nearest whole number.

Step-by-step 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 = 100

r = 2.5% = 2.5/100 = 0.025

t = 12 years

Therefore,

A = 100 x 2.7183^ (0.025 x 12)

A = 100 x 2.7183^ (0.3)

A = $135.0 to the nearest cent