Final answer:
To find the compound amount for a $700 investment over 8 years at 11% compounded monthly, use the formula A = P(1 + r/n)^(nt) and substitute the values accordingly. After calculations, the compound amount is approximately $1,448.05.
Step-by-step explanation:
To find the compound amount for the given investment, we will use the formula for compound interest:
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.
t is the time the money is invested for, in years.
For this particular problem:
P = $700
r = 11% or 0.11
n = 12 (since the interest is compounded monthly)
t = 8 years
Now, we substitute the values into the formula:
A = 700(1 + 0.11/12)^(12*8)
A = 700(1 + 0.0091667)^(96)
A = 700 * (1.0091667)^96
Around off to two decimal places, A = $1,448.05 (your calculated amount might slightly differ due to rounding)
The total compound amount after 8 years is approximately $1,448.05.
This example illustrates how compound interest can significantly increase an investment over time, especially when compared to simple interest.