How much will you have accumulated, if you annually invest $1,500 into an IRA at 8% interest compounded monthly for 5 year?
To calculate the accumulated amount in an IRA with an annual investment of $1,500 at 8% interest compounded monthly for 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the accumulated amount
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case:
P = $1,500
r = 8% = 0.08
n = 12 (since interest is compounded monthly)
t = 5
Substituting these values into the formula, we get:
A = $1,500(1 + 0.08/12)^(12*5)
To simplify this equation, let's first calculate (1 + 0.08/12):
(1 + 0.08/12) = 1.0066667
Now, substitute this back into the formula:
A = $1,500 * (1.0066667)^(12*5)
Now, raise (1.0066667) to the power (12*5):
(1.0066667)^(12*5) ≈ 1.46933
Finally, multiply this by the initial investment:
A ≈ $1,500 * 1.46933
A ≈ $2,203
Therefore, if you annually invest $1,500 into an IRA at 8% interest compounded monthly for 5 years, you will accumulate approximately $2,203.