Suppose consumers only hold checkable deposits. The demand for money for transactions by consumers is equal to Y*(0.3 - i), where i is in decimals. Income is 800, and the reserve ratio of banks is 0.4. The supply of currency by the central bank is 40. What is the equilibrium interest rate

17.5%

Explanation:

The equilibrium will occur where the money demanded equals to the money supplied i.e Ms = Md

From the question, the supply of currency by the Central Bank = 40

Money Supply (Ms) = m × B

where m = Money multiplier = 2.5

Note that the money multiplier can also be equal to 1/rr in situations wherebt the consumers do not hold any currency.

rr = reserve ratio, = 0.4

B = monetary base = 40

Note that the monetary base here is 40.

Since reserve ratio = 0.4, therefore

m = 1/0.4 = 2.5

Therefore, Ms = m × B

= 2.5 × 40

= 100

Thus Money supply Ms = 100.

Money demand(Md) = Y(0.3 - i),

Y = income = 800

i = interest rate

Since (Md) = Y(0.3 - i),

Md = 800(0.3 - i)

Equate the equation for the money demand and money supply together.

Ms = Md

100 = 800(0.3 - i)

100 = 240 - 800i

800i = 240 - 100

800i = 140

i = 140/800

i= 0.175

= 17.5%

Therefore, the interest rate is 17.5%

month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

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