Question

Karen borrowed $8000 at a rate of 11.5%, compounded semiannually. How much will she owe after 7 years?

A) $16,243.44
B) $17,523.89
C) $18,041.60
D) $18,670.25

Answer 1

Main Answer:

Karen's compounded semiannual loan of $8000 at 11.5% for 7 years yields $18,041.60, making the correct answer C.C) $18,041.60

Explanation:

Karen borrowed $8000 at a rate of 11.5%, compounded semiannually. To calculate the future value, we use the compound interest formula:
`\(A = P \left(1 + (r)/(n)\right)^(nt)\)`, where
`\(A\)` is the future value,
`\(P\)` is the principal amount,
`\(r\)` is the annual interest rate (as a decimal),
`\(n\)` is the number of times interest is compounded per year, and
`\(t\)` is the number of years. In this case,
`\(P = $8000\), \(r = 0.115\), \(n = 2\) (compounded semiannually),` and
`\(t = 7\)`. Plugging in these values into the formula gives us:
`\[A = 8000 \left(1 + (0.115)/(2)\right)^(2 * 7) = $18,041.60\]`

Therefore, Karen will owe $18,041.60 after 7 years.Compound interest, as opposed to simple interest, takes into account the interest earned on previously accrued interest. In this case, the semiannual compounding amplifies the growth. The more frequent compounding periods lead to a higher effective interest rate, resulting in a greater final amount owed. This illustrates the importance of understanding compounding frequencies when calculating the future value of a loan.

Therefore, the correct answer is C) $18,041.60.