Question

What is the future value of $1,200 invested for 20 years at a rate of 6%?
a) $1,440
b) $1,849
c) $3,079
d) $3,849

Answer 1

Answer: d) $3,849

Step-by-step explanation:

To calculate the future value of an investment, we can use the formula for compound interest. Let V be the future value, P be the principal amount, r be the interest rate, and t be the time.

        $\displaystyle V=P(1+r)^n$

Substitute known values.

        $\displaystyle V=(1,200)(1+0.06)^{20}$

Addition:

        $\displaystyle V=(1,200)(1.06)^{20}$

Raise to the 20th power:

        $\displaystyle V=(1,200)(3.207135)$

Multiply and round the nearest dollar:

        $\displaystyle V=\ 3,849$

Answer 2

Final answer:

The future value of a $1,200 investment at a 6% interest rate for 20 years is found using the compound interest formula and results in approximately $3,849. The correct choice is (d).

Explanation:

The subject of the question is to calculate the future value of an investment given a fixed interest rate and a specific time period. We can use the formula for compound interest to determine the future value of this investment:

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

Where:

• FV is the future value of the investment
• P is the principal amount (the initial amount of money)
• r is the annual interest rate (in decimal form)
• n is the number of times that interest is compounded per year
• t is the number of years the money is invested

For this particular problem, the principal amount P is $1,200, the annual interest rate r is 6% (or 0.06 in decimal form), compounded annually (n = 1), and the time period t is 20 years.

Let's plug these values into the formula:

FV = $1,200(1 + 0.06/1)^(1*20)

FV = $1,200(1 + 0.06)^20

FV = $1,200(1.06)^20

FV = $1,200(3.207135)

FV = $3,848.56 (rounded to the nearest dollar)

Therefore, the future value of $1,200 invested for 20 years at a rate of 6% is approximately $3,849, making the correct answer (d).