Find the accumulated value of an investment of $700 at 16%compounded quarterly for 2 years.
16%compounded quarterly for 2 years.
----> i = .08, n = 4
Amount = 700(1.08)^4
= ....
I don't know why I read that as semi-annually
so
i = .04
n = 8
amount = 700(1.04)^8
= 958.00
To find the accumulated value of an investment, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Accumulated value
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
In this case, the principal amount (P) is $700, the annual interest rate (r) is 16% (or 0.16 as a decimal), the interest is compounded quarterly (n = 4), and the investment duration (t) is 2 years.
Now, let's plug in the values into the formula:
A = 700(1 + 0.16/4)^(4*2)
First, let's simplify the exponent:
A = 700(1 + 0.04)^8
Next, let's calculate the value inside the parentheses:
A = 700(1.04)^8
Now, let's calculate the exponent:
A = 700(1.425971)
Finally, let's calculate the accumulated value:
A ≈ $997.18 (rounded to the nearest cent)
So, the accumulated value of an investment of $700 at an annual interest rate of 16%, compounded quarterly for 2 years, is approximately $997.18.