suppose that $3500 is borrowed for three years at an interest rate of 4% per year. compounded continuously. find the amount owed, assuming no payments are made till the end. Round to the nearest cent.
3500 * e^(.04*3)
3946.24
A=P(1+r/n)^(nt)
P=3500, r=4%=0.04,t=3,n=1
A=3500(1+(0.04/1))^(3×1)=3500(1.04)^3
A=3500(1.124864)=3937.024=3937.00 (rounded to nearest cent)
Your calculation is correct, but I think there's a small error in the final rounding. The amount owed should be rounded to $3937.02 to the nearest cent.
To find the amount owed when $3500 is borrowed for three years at a continuous interest rate of 4% per year, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the amount owed
P = the principal amount (initial loan amount)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (expressed as a decimal)
t = the time period (in years)
Let's calculate the amount owed step by step:
Step 1: Convert the annual interest rate to a decimal:
The annual interest rate is 4%. To convert it to a decimal, divide by 100:
r = 4% / 100 = 0.04
Step 2: Plug in the values into the formula and calculate:
A = P * e^(rt)
A = $3500 * e^(0.04 * 3)
Here, e^(0.04 * 3) represents the value of e raised to the power of (0.04 * 3).
Using a calculator:
A = $3500 * e^(0.04 * 3) ≈ $3500 * e^(0.12) ≈ $3500 * 1.12749685 ≈ $3946.74
Therefore, the amount owed, assuming no payments are made until the end of three years, is approximately $3946.74 when rounded to the nearest cent.