Question

Rochelle deposits $6,000 in an IRA. What will be the value (in dollars) of her investment in 15 years if the investment is earning 6% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)

Answer 1

To calculate the value of Rochelle's investment in 15 years with continuous compounding, we use the formula A = P * e^(rt). Plugging in the given values, the investment will be approximately $12,797.66.

Step-by-step explanation:

To calculate the value of Rochelle's investment in 15 years, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

• A is the final amount
• P is the principal amount
• e is Euler's number (approximately 2.71828)
• r is the interest rate per year
• t is the time in years

Plugging in the given values:

A = 6000 * e^(0.06 * 15)

Using a calculator or spreadsheet, we find that the value of Rochelle's investment after 15 years is approximately $12,797.66.

Answer 2

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.

From the information given,

P = $6000

r = 6% = 6/100 = 0.06

t = 15 years

Therefore,

A = 6000 x e(0.06 x 15)

A = 6000 x e(0.9)

A = $14757.6 to the nearest cent