Question

Find the accumulated value of an investment of $8,000 at 12% compounded annually for 17 years.

Answer 1

The accumulated value of an $8,000 investment at a 12% interest rate compounded annually for 17 years is $43,381.60, calculated using the compound interest formula.

Step-by-step explanation:

The student is requesting to find the accumulated value of an investment of $8,000 at a 12% annual interest rate, compounded annually for 17 years. To solve this, we use the compound interest formula, which is A = P(1 + 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, and t is the time the money is invested for in years.

To apply the formula for compound interest:
A = $8,000(1 + 0.12/1)1*17
A = $8,000(1 + 0.12)17
A = $8,000(1.12)17
A = $8,000 * (5.4227)
A = $43,381.60

Therefore, the accumulated value of the investment after 17 years is $43,381.60.

Answer 2

After 17 years of compounding interest at 12% annually, your initial investment of $8,000 will grow to roughly $54,928.

To find the accumulated value of an investment of $8,000 at 12% compounded annually for 17 years, we can use the compound interest formula:

`A=P(1+r / n)^(\wedge)(n t)`

where:

A is the accumulated value

P is the principal amount (initial investment)

r is the annual interest rate

n is the number of compounding periods per year (in this case, 1 since it's compounded annually)

t is the total number of years

In this case:

P = $8,000

r = 12% (converted to decimal: 0.12)

n = 1

t = 17

Plugging these values into the formula, we get:

A = $8,000 (1 + 0.12/1) ^ (1 * 17)

A ≈ $54,928.33

Therefore, the accumulated value of the investment after 17 years is approximately $54,928.33.