what is the effective interest rate of a simple discount note for $31,700, at an ordinary bank discount rate…

what is the effective interest rate of a simple discount note for $31,700, at an ordinary bank discount rate of 10%, for 30 days? assume that there are 360 days in a year.\n\neffective interest rate is (%) (round to the nearest tenth as needed.)

what is the effective interest rate of a simple discount note for $31,700, at an ordinary bank discount rate of 10%, for 30 days? assume that there are 360 days in a year.\n\neffective interest rate is (%) (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Calculate the bank discount

The formula for bank discount $D$ is $D = M\times d\times t$, where $M$ is the maturity value, $d$ is the discount rate, and $t$ is the time in years. Here, $M=$31700$, $d = 0.10$, and $t=\frac{30}{360}$. $D=31700\times0.10\times\frac{30}{360}=\frac{31700\times0.10\times30}{360}=\frac{95100}{360}\approx264.17$

Step2: Calculate the proceeds

The proceeds $P$ is $P = M - D$. So $P=31700 - 264.17 = 31435.83$

Step3: Calculate the effective - interest rate

The formula for the effective - interest rate $r$ is $r=\frac{D}{P\times t}$. Substitute $D\approx264.17$, $P = 31435.83$, and $t=\frac{30}{360}$ into the formula. $r=\frac{264.17}{31435.83\times\frac{30}{360}}=\frac{264.17\times360}{31435.83\times30}=\frac{95101.2}{943074.9}\approx0.101$ or $10.1%$

Answer:

$10.1$