Find the accumulated amount A if the principal, P = $3700 is invested at the interest rate r = 7%/year for t = 12.5 years compounded semiannually. Round your answers to two decimal places.
a. The accumulated amount is $8544.01.
b. The accumulated amount is $8592.56.
c. The accumulated amount is $8,744.01.
d. The accumulated amount is $8644.01.
e. The accumulated amount is $8509.62.
Thank you
3700(1 + .07/2)^(2*12.5) = ?
$8744.1
To find the accumulated amount A, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = accumulated amount
P = principal amount
r = interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $3700
r = 7% = 0.07 (as a decimal)
t = 12.5 years
n = 2 (compounded semiannually)
Substituting the values into the formula, we get:
A = 3700(1 + 0.07/2)^(2*12.5)
A = 3700(1.035)^(25)
Using a calculator, we find:
A ≈ $8592.56
So the correct answer is b. The accumulated amount is $8592.56.
To find the accumulated amount A, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, P = $3700, r = 7% = 0.07 (as a decimal), n = 2 (since it's compounded semiannually), and t = 12.5 years.
Plugging in these values into the formula, we can calculate the accumulated amount A:
A = $3700(1 + 0.07/2)^(2 * 12.5)
= $3700(1 + 0.035)^(25)
= $3700(1.035)^(25)
= $3700(1.983295632)
= $7333.88
Therefore, the correct answer is none of the options provided. The accumulated amount A is $7333.88.