Use the compound interest formulas A = P(1 + r/n)nt and A = Pe^rt to solve.
Find the accumulated value of an investment of $3000 at 9% compounded continuously for 3 years.
what's the problem? You have the formula and the numbers. Plug and chug. The only hard part is picking the proper formula.
We'll be happy to check what you get.
To find the accumulated value using the formula A = Pe^rt, where A is the accumulated value, P is the principal amount, r is the interest rate, t is the time in years, and e is Euler's number approximately equal to 2.71828.
Step 1: Identify the given values:
P = $3000 (principal amount)
r = 9% (interest rate in decimal form, so divide by 100)
t = 3 years (time in years)
Step 2: Plug the values into the formula A = Pe^rt:
A = $3000 * e^(0.09 * 3)
Step 3: Calculate the value inside the exponent:
0.09 * 3 = 0.27
Step 4: Calculate e^0.27 using a calculator:
e^0.27 ≈ 1.3107962
Step 5: Multiply the principal amount by the result from Step 4:
A = $3000 * 1.3107962
Step 6: Calculate the accumulated value:
A ≈ $3,932.3886
Therefore, the accumulated value of an investment of $3000 at 9% compounded continuously for 3 years is approximately $3,932.39.