Question

Suppose that $2000 is loaned at a rate of 11.5%, compounded annually. Assuming that no payments are made, find the amount owed after 8 years.

Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

$4,777.81

Explanation:

Interest is money gained on an initial investment or loan.

Compound Interest

Interest is when the amount owed increases at a certain rate. In compound interest, the amount of interest earned increases periodically. In this case, the loan is compounded once a year. Additionally, the amount owed increases at a rate of 11.5% per year. The formula to solve compound interest is:

• 
  `\displaystyle A = P(1+ (r)/(n) )^(nt)`

In this formula, P is the principal, r is the rate as a decimal, n is the number of times compounded per year, and t is the time in years.

Solving for Amount Owed

To find A, all we need to do is plug in the information we know. However, since n is 1, we can ignore it in the equation.

• A = 2000(1 + 0.115)⁸
• A = 4,777.81

This means given the interest rate, $4,777.81 will be owed.