Find the principal when the amount in the account is 11,000 and rate of interest is 3.45 percent compounded interest is quarterly for 2.5 years.
P(1+0.0345/4)^(4*2.5) = 11000
P = 10094.75
To find the principal when the amount in the account is $11,000 and the interest rate is 3.45% compounded quarterly for 2.5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the amount after time t
P = the principal or initial amount
r = the interest rate (in decimal form)
n = the number of compounding periods per year
t = the time period (in years)
In this case:
A = $11,000 (the amount in the account after 2.5 years)
r = 3.45% = 0.0345 (interest rate in decimal form)
n = 4 (quarterly compounding, as there are 4 quarters in a year)
t = 2.5 years
Let's rearrange the formula and solve for P (the principal):
P = A / (1 + r/n)^(n*t)
Substituting the given values:
P = $11,000 / (1 + 0.0345/4)^(4*2.5)
Calculating the expression inside the parentheses:
P = $11,000 / (1 + 0.008625)^(10)
Now, let's simplify:
P = $11,000 / (1.008625)^(10)
Using a calculator or spreadsheet software, we can raise (1.008625) to the power of 10 and divide $11,000 by the result to find the principal.
P ≈ $9,548.79
Therefore, the principal (initial amount) is approximately $9,548.79.