Suppose Annie expects an annual return of $520 from an investment worth $500.What should be the rate of interest charged by her to a risky borrower who is likely to repay the principal and interest with a probability of 0.7?
A)45 percent
B)48.6 percent
C)20.33 percent
D)53.4 percent

Question

Quizplus · Accepted Answer

To find the rate of interest $ r $ that Annie should charge, we use the expected return formula. Given that the expected return is $520 from a $500 investment, and the probability of repayment is 0.7, we set up the equation:$$ 500 \times (1 + r) \times 0.7 = 520 $$Solving for $ r $:$$ 350 + 350r = 520 $$$$ 350r = 170 $$$$ r = \frac{170}{350} = 0.4857 $$Converting to percentage:$$ r = 48.57\% $$Rounded to one decimal place, the rate of interest Annie should charge is approximately 48.6 percent.

Suppose Annie Expects an Annual Return of $520 from an Investment