find the amount of money in an account after 10 years if a principal of $2500 is invested at 3.5% interest compounded quarterly.
show work please I got 2250 but my book shows 3542.27
Use
Amount = principal * (1+i)^n
principal=initial investment
number of periods (of 3 months) = 10*4=40
i=interest per period = 3.5%/4=0.00875
To find the amount of money in an account after 10 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the total amount after the given time period)
P = the principal amount (the initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Let's use this formula to find the correct answer:
P = $2500 (given principal amount)
r = 3.5% (annual interest rate, expressed as 0.035)
n = 4 (quarterly compounding means 4 times per year)
t = 10 (number of years)
Substituting these values into the formula:
A = 2500(1 + 0.035/4)^(4*10)
A = 2500(1 + 0.00875)^(40)
A = 2500(1.00875)^(40)
A = 2500(1.481267034)
A ≈ $3,703.17
The correct amount of money in the account after 10 years is approximately $3,703.17, not $2,250 or $3,542.27. Double-check your calculations or consult the solution provided here for verification.