Question

Find the accumulated amount of an investment of $15000 for 5 years at 6.2% compounded monthly?

Answer 1

The accumulated amount of a $15000 investment at 6.2% interest compounded monthly for 5 years is calculated using the compound interest formula. The end result is $20,232.85.

Step-by-step explanation:

The question relates to calculating the accumulated amount of a compound interest investment. To find the accumulated amount of a $15000 investment at 6.2% interest compounded monthly for 5 years, we can use the compound interest formula:

A = P (1 + \frac{r}{n})^{nt}

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time in years.

Here's how we can calculate:

P = $15000

r = 6.2% or 0.062 (as a decimal)

n = 12 (since the interest is compounded monthly)

t = 5 years

Now, we plug these values into the formula to find A:

A = 15000 (1 + \frac{0.062}{12})^{(12 \times 5)}

A = 15000 (1 + 0.0051667)^{60}

A = 15000 (1.0051667)^{60}

A = 15000 \times 1.348857

A = $20,232.85 (rounded to two decimal places)

The accumulated amount after 5 years is $20,232.85.

Answer 2

The accumulated amount of an investment of $15000 for 5 years at a 6.2% annual interest rate compounded monthly is approximately $20,356.36.

Explanation:

To determine the accumulated amount (A) of an investment, the formula for compound interest A = P(1 + r/n)^(nt) is used, where:

- P represents the principal amount ($15,000 in this case).

- r represents the annual interest rate in decimal form (6.2% becomes 0.062).

- n represents the number of times that interest is compounded per year (monthly compounding means n = 12).

- t represents the time the money is invested for in years (5 years in this case).

Substituting the values into the formula, A = 15000(1 + 0.062/12)^(12*5), calculates to A ≈ $20,356.36. This result shows the total amount after 5 years, accounting for monthly compounding of interest. The formula accounts for the monthly interest earned on both the initial investment and the interest earned in previous months, leading to the final accumulated amount.

The concept of compounding interest frequently leads to higher returns on investments over time compared to simple interest. In this case, the investment of $15,000 at an annual interest rate of 6.2% compounded monthly has accumulated to approximately $20,356.36 after 5 years. The frequent compounding periods enable the investment to grow significantly due to the interest being added to the principal amount each month, resulting in a higher total accumulated amount than simple interest over the same period.