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A man borrowed from a bank a promissory note that he signed in the amount of 25000 for a period of one year. He received only the amount 21915 after the bank collected the advance interest and an additional amount of 85.00 for the inspection fee. What was the rate of discount, the rate of interest that the bank collected in advance?

The Answer is 12%, 13.64%

Interest, I = Principal,P * rate of interest,i * number of the interest period, n

I = 25000-(21915+85) = 3000

I = Pin; 3000 = 25000*i*1; i = 0.12

Relationship between rate of discount and rate of interest:

d = 1-(1+i)^-1
d = 1-(1+0.12)^-1 = 0.1071

Any hint on what am i doing wrong?

james
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1 Answers1

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First of all you havn´t a perfect capital market, because you have transaction costs. In this case they are 85. The man has to pay the transaction costs. The man wants to borrow 21,915. He has to pay a fee of 85. Therefore he has to borrow in total 22,000. Let denote it $C_0$. After one year he has to pay back 25,000($C_1$).

Relation between $C_1, C_0$ and discount rate:

$C_0=(1-d)\cdot C_1$

Solving for d

$d=\frac{C_1-C_0}{C_1}=\frac{C_1-C_0}{C_1}\cdot 100\%$

In words:" How much is $C_0$ less than $C_1$ in relation to $C_1$.

$d=\frac{25,000-22,000}{25,000}\cdot 100\%=12\% $

Relation between $C_1, C_0$ and interest rate:

$C_1=(1+i)\cdot C_0$

Solving for i:

$i=\frac{C_1-C_0}{C_0}=\frac{C_1-C_0}{C_0}\cdot 100\% $

In words:" How much is $C_1$ bigger than $C_0$ in relation to $C_0$.

$i=\frac{25,000-22,000}{22,000}\cdot 100\%\approx 13.46\% $

The relation between i and d is:

$\boxed{d=\frac{i}{1+i}}$

Or

$i=\frac{d}{1-d}$

callculus42
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