An individual spends $5 daily and also spends an additional $1.50 each time he goes to an ATM.There is also a 12 percent risk of having his cash lost or stolen.If his total cost of holding cash is (547.50/T) + (0.375 × T), then what is the ongoing nominal interest rate in the economy? Assume that the individual visits the ATM once in every T days.
A)1 percent.
B)2 percent.
C)3 percent.
D)4 percent.

Question

Quizplus · Accepted Answer

First, we need to calculate the total cost of holding cash over a year:

Daily cost = $5 + $1.50 = $6.50
Annual cost = $6.50 * 365 = $2,372.50

Now, we need to take into account the 12% risk of loss or theft:

Effective annual cost = $2,372.50 * (1 + 0.12) = $2,657.00

Finally, we can use this equation to solve for the nominal interest rate (r):

Effective Annual Interest Rate = (1 + r/n)^n - 1

where n is the number of times interest is compounded per year. Since we visit the ATM once in every T days, the number of times interest is compounded per year is:

n = 365/T

Plugging in the values, we get:

(1 + r/(365/T))^(365/T) - 1 = $2,657.00/$547.50

Solving for r using trial and error, we get:

r = 0.03 or 3%

Therefore, the answer is C) 3 percent.

An Individual Spends $5 Daily and Also Spends an Additional