Exponentivi and Logarleunic Functions
Finding the final amount in a word problem on continuous compound._.
A certain loan program offers an interest rate of $3.5 \%$ per year, compounded continuously. Assuming no payments are made, how much would be owed after six years on a loan of $\$ 1100$ ?
Do not round any intermediate computations, and round your answer to the nearest cent.
s[1]
$\times$
5
Answer
Final Answer: The amount owed after six years on a loan of $1100 with an interest rate of 3.5% per year, compounded continuously, would be \(\boxed{1357.05}\)
Step 1 ：The problem is asking for the final amount owed after six years on a loan of $1100 with an interest rate of 3.5% per year, compounded continuously.
Step 2 ：The formula for continuous compounding is \(A = P * e^{rt}\), where: \(A\) is the amount of money accumulated after n years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), and \(t\) is the time the money is invested for, in years.
Step 3 ：In this case, \(P = 1100\), \(r = 3.5/100 = 0.035\) (converted from percentage to decimal), and \(t = 6\) years.
Step 4 ：We can substitute these values into the formula and calculate the final amount: \(A = 1100 * e^{(0.035 * 6)}\)
Step 5 ：Calculating the above expression gives \(A = 1357.05\)
Step 6 ：Final Answer: The amount owed after six years on a loan of $1100 with an interest rate of 3.5% per year, compounded continuously, would be \(\boxed{1357.05}\)
