Suppose that $2000 is loaned at a rate of 13.5%, compounded annually. Assuming that no payments are made, find the amount owed after 9 years.Do not round any intermediate computations, and round your answer to the nearest cent.$
Solution
To solve this problem, we will use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, the loan is compounded annually, so n = 1. The principal amount P is $2000, the annual interest rate r is 13.5% or 0.135 in decimal form, and the time t is 9 years.
Substituting these values into the formula, we get:
A = 2000 (1 + 0.135/1)^(1*9) A = 2000 (1.135)^9
Now, calculate the value inside the parentheses:
1.135^9 = 3.39107
Then multiply this by the principal amount:
A = 2000 * 3.39107 = $6782.14
So, the amount owed after 9 years would be approximately $6782.14.
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