An investment account earns 4% per year compounded annually. If the initial investment was $4,000.00, how much is in the account after 3 years? Round your answer to the nearest dollar.
Im assuming that what i would do here is find out what 4 percent of 4,000 is, then add/multiply (not sure which one) by 3, then round.
Can someone please tell me what 4 percent of 4,000.00 is, and lemme know if this is the correct way to solve this problem?
Your "4% per year compounded annually" is the give-away that you are dealing with compound interest.
amount = principal (1+i)^n
= 4000(1.04)^3
= 4000(1.124864) = 4499.46 or 4500 to the nearest dollar as asked for
What you were planning to do would be "simple interest"
.04(4000) = $160 per year
so for 3 years ---> $480
so using simple interest you would have $4480 , a difference of $20
Actually $4499.46 to the nearest dollar would be $4499
This Actually helped alot thanks!!!!!!!
To calculate the amount in the investment account after 3 years with a 4% interest rate compounded annually, you would use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the initial investment (P) is $4,000, the annual interest rate (r) is 4% or 0.04 (as a decimal), the interest is compounded annually, so n = 1, and the time (t) is 3 years.
Plugging in these values to the formula, we have:
A = 4,000(1 + 0.04/1)^(1*3)
A = 4,000(1 + 0.04)^3
A = 4,000(1.04)^3
A ≈ 4,000(1.124864)
A ≈ 4,499.46
Therefore, the amount in the account after 3 years would be approximately $4,499.46.
To round the answer to the nearest dollar, we round the value to the nearest whole number:
Rounded Amount = $4,499
So, the amount in the account after 3 years would be $4,499.