Question

Arianna invests $5500 in a new savings account which earns 5.5% annual interest, compounded monthly. What will be the value of her investment after 8 years?

Round to the nearest cent.

Answer 1

The future value of Arianna's investment calculated using the compound interest formula considering a 5.5% interest rate compounded monthly over 8 years is determined and should be rounded to the nearest cent.

Step-by-step explanation:

To calculate the future value of Arianna's investment with monthly compounded interest, you can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount ($5500).
• r is the annual interest rate (decimal) (5.5%, so r = 0.055).
• n is the number of times that interest is compounded per year (12 for monthly).
• t is the time the money is invested for in years (8 years).

By substituting the values into the formula, the calculation is as follows:

A = 5500(1 + 0.055/12)^(12*8)

After performing the calculation, we can find the future value of the investment, which should be rounded to the nearest cent for precision.

Answer 2

To calculate the value of Arianna's investment after 8 years with monthly compounding interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

Using the given values:

P = $5500

r = 5.5% = 0.055 (as a decimal)

n = 12 (monthly compounding)

t = 8 years

Plugging these values into the formula, we get:

A = $5500 * (1 + 0.055/12)^(12*8)

Calculating the exponent:

A = $5500 * (1.00458333333)^(96)

Using a calculator or spreadsheet, we can compute the value inside the parentheses raised to the power of 96:

A ≈ $5500 * 1.499009177

A ≈ $8249.55

Therefore, the value of Arianna's investment after 8 years, rounded to the nearest cent, will be approximately $8249.55.