Find the ending balance in an account that opens with $3,180, earns 11.5% interest compounded monthly, and is held for 20 years. (Round your answer to the nearest cent.)
B=p(12+r)^n
B=3,180(12+0.95)^20
B=1,759.52
Is this correct if not, can someone help me with the steps.
It is not correct. Why would you end up with less money after 20 years of earning interest? True, our banks are ripping us off, but they aren't THAT bad.
Your starting equation is wrong. So are your later calculations. Where did the 0.95 come from?
With monthly compounding 240 times,
B = P*[1 + (r/12)]^240
= 3180*[1.009583333]^240
= $ 31,372.45
Thanks,drwls I see where I made a mistake with the 0.95 but where did the 240 come from.
To calculate the ending balance in an account with compound interest, you can use the formula:
B = P(1 + r/n)^(nt)
Where:
B = Ending balance
P = Principal amount (initial balance)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years the money is invested for
Let's break down the steps to calculate the ending balance in your case:
Principal amount (P) = $3,180
Annual interest rate (r) = 11.5% --> Convert it to a decimal by dividing by 100: r = 0.115
Number of times interest is compounded per year (n) = 12 (monthly compounding)
Number of years (t) = 20
Substituting these values into the formula:
B = 3,180(1 + 0.115/12)^(12*20)
B = 3,180(1 + 0.009583333)^240
Now, calculate the value inside the parentheses:
(1 + 0.009583333) = 1.009583333
Next, raise this value to the power of 240:
(1.009583333)^240 = 1.950855413
Finally, multiply this result by the principal amount:
B = 3,180 * 1.950855413 ≈ $6,184.29
So, the correct ending balance in the account after 20 years, with monthly compounding at an 11.5% interest rate, is approximately $6,184.29 (rounded to the nearest cent).