Suppose that $2000 is loaned at a rate of 16%, compounded quarterly. Assuming that no payments are made, find the amount owed after 8 years.Do not round any intermediate computations, and round your answer to the nearest cent.$
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
Given in the problem: P = $2000 r = 16% or 0.16 (in decimal) n = 4 (since the interest is compounded quarterly) t = 8 years
Substitute these values into the formula:
A = 2000 (1 + 0.16/4)^(4*8)
Now, calculate the expression inside the parentheses:
A = 2000 (1 + 0.04)^32
A = 2000 (1.04)^32
Now, raise 1.04 to the power of 32:
A = 2000 * 3.243409153
Finally, multiply 2000 by 3.243409153 to find the total amount owed after 8 years:
A = $6486.82
So, the amount owed after 8 years would be approximately $6486.82.
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