Question

Francis deposits $11,000 in an IRA. What will be the value of his investment in 9 years if the investment is earning 4.1% per year and is compounded continuously? Round your answer to the nearest cent.

Answer 1

The value of Francis's $11,000 IRA investment after 9 years with a continuous compound interest rate of 4.1% will be approximately $15,915.35.

Step-by-step explanation:

To calculate the future value of an investment compounded continuously, we need to use the formula Pert, where P is the principal amount, 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). Given Francis's IRA deposit of $11,000, an interest rate of 4.1%, and a time period of 9 years, we can plug these values into the formula to find the future value.

First, we convert the interest rate to a decimal by dividing by 100: r = 4.1 / 100 = 0.041.

Next, we use the formula to calculate the value:

Future Value = 11,000 * e0.041 * 9

Using a calculator with an ex function, we get:

Future Value = 11,000 * e0.369

Future Value ≈ $11,000 * 1.44685 ≈ $15,915.35

So, after 9 years of continuous compounding at an annual rate of 4.1%, the value of Francis's investment will be approximately $15,915.35 when rounded to the nearest cent.

Answer 2

The value of Francis's investment after 9 years would be approximately $15,906.48 rounded to the nearest cent.

The future value of an investment compounded continuously, you can use the formula:

A = P · e^{rt}

where:

A is the future value of the investment

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

t is the time the money is invested for in years

e is the mathematical constant approximately equal to 2.71828

In this case:

P = $11,000

r = 4.1% or 0.041 (as a decimal)

t = 9 years

Now, plug these values into the formula:

A = 11000 · e^{0.041 · 9}

Calculate the result:

A ≈ 11000 · e^{0.369}

A ≈ 11000 · 1.446

A ≈ 15,906.48

So, the value of Francis's investment after 9 years would be approximately $15,906.48 rounded to the nearest cent.