Suppose that you invest $ 300 per month in a saving account for the next 30 years which earns 0.12 per year, what is the value of the investment today?chegg
To calculate the value of the investment today, we need to use the future value of an annuity formula. The future value of an annuity formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the investment
P = Monthly investment amount
r = Annual interest rate
n = Number of years
In this case, the monthly investment amount is $300, the annual interest rate is 0.12, and the number of years is 30.
Let's plug in the values into the formula:
FV = 300 * ((1 + 0.12)^30 - 1) / 0.12
First, let's calculate (1 + 0.12)^30 - 1:
(1 + 0.12)^30 - 1 ≈ 5.5242
Now, let's calculate the future value:
FV = 300 * 5.5242 / 0.12 ≈ $13,161.67
Therefore, the value of the investment today is approximately $13,161.67.