Suppose that $2000 is loaned at a rate of 15%, compounded annually. Assuming that no payments are made, find the amount owed after 5 years.Do not round any intermediate computations, and round your answer to the nearest cent.$
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 loaned amount (P) is $2000, the annual interest rate (r) is 15% or 0.15 in decimal, the interest is compounded annually so n is 1, and the time (t) is 5 years.
Substituting these values into the formula, we get:
A = 2000 (1 + 0.15/1)^(1*5) A = 2000 (1 + 0.15)^5 A = 2000 * 1.15^5
Now, calculate the value of 1.15^5, then multiply the result by 2000 to get the total amount owed after 5 years.
Remember to round your final answer to the nearest cent.
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