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.
Can someone help please?
Semi-annually means the money is looked at twice a year (for each of the three years), and the interest at 4% is split into 2 (for semi-annually) each year so...
A = P(1 + i)^n
A=4000( 1 + 0.04/2)^(3x2)
....
Solve for the accumulated amount in the account.
but it said compounded annually, so
A=4000( 1 + 0.04)^3
OOOOPS! so sorry! I thought it was compounded SEMI-ANNUALLy! So very sorry. Thanks for the proper solution Reiny : )
ohhh ok thank you guys!!!
Sure! I can help you with that. To determine the final amount in the investment account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount after time t,
P is the initial amount (principal),
r is the annual interest rate (as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, the initial investment (P) is $4,000.00, the annual interest rate (r) is 4% or 0.04 (as a decimal), the interest is compounded annually, so n = 1, and the time period (t) is 3 years.
Plugging these values into the formula, we get:
A = 4000(1 + 0.04/1)^(1*3)
Simplifying the expression inside the parentheses:
A = 4000(1 + 0.04)^3
Calculating the value inside the parentheses:
A = 4000(1.04)^3
A = 4000(1.124864)
A ≈ 4499.46
Rounded to the nearest dollar, the amount in the investment account after 3 years would be $4,499.
Note: Some calculators and software may provide more decimal places, so it's always a good idea to round to the appropriate number of decimal places or significant figures based on the context of the problem.