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Question ONE (Total: 8 marks: 2 marks each) Suppose Tiger Bank's initial balanc...
Apr 6, 2024
Question ONE (Total: 8 marks: 2 marks each) Suppose Tiger Bank's initial balance sheet is as follows (in millions). The cument required reserve ratio is ONLY 10I410 \mathrm{I}_{4}. \begin{tabular}{|c|c|c|c|} \hline \multicolumn{2}{|l|}{ Asouts } & \multicolumn{2}{|l|}{ Liabulities } \\ \hline Kesurnes & (sui) & Drposit & 85,040 \\ \hline Loans & $2.200\$ 2.200 & Equity & 5300 \\ \hline Secunties & $2,500\$ 2,500 & & \\ \hline TOTAL. & 55,3110 & Toral. & 55,3100 \\ \hline \end{tabular} a) What is the bank"s requirod reserse? b) Tiger Bark runs into a hage withdruwal of SSOMM. Describe in option then is available for the bank to mitigase this problem basod on Purchase Liquidity Management. Sbow this balmee sheet, assume the bank only kecps the minimam required reserve. c) Tiger Bank runs into a huge withdrawal of 5500M. Show the balance sheet if the bank only keeps the minimum required reserve. d) Banks can minimize losses by adding restrictive onvenant to the loan aprocments. State any TWO different types of covenants that can redowe moral havard problems.
Solution by Steps
step 1
Given the differential equation ddt(43πr3)=−2π\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right) = -2\pi, we need to solve for drdt\frac{dr}{dt} when r=5r=5
step 2
Differentiate 43πr3\frac{4}{3}\pi r^3 with respect to tt to get 4πr2drdt4\pi r^2 \frac{dr}{dt}
step 3
Set the derivative equal to −2π-2\pi, resulting in 4πr2drdt=−2π4\pi r^2 \frac{dr}{dt} = -2\pi
step 4
Substitute r=5r=5 into the equation to solve for drdt\frac{dr}{dt}, yielding 4π(5)2drdt=−2π4\pi (5)^2 \frac{dr}{dt} = -2\pi
step 5
Simplify the equation to find drdt\frac{dr}{dt}, which gives drdt=−2π4π(5)2\frac{dr}{dt} = \frac{-2\pi}{4\pi (5)^2}
step 6
Calculate drdt\frac{dr}{dt} to get drdt=−2π100π=−150\frac{dr}{dt} = \frac{-2\pi}{100\pi} = \frac{-1}{50}
Answer
drdt=−150\frac{dr}{dt} = \frac{-1}{50} when r=5r=5
Key Concept
Solving a differential equation for a specific variable
Explanation
We solved the differential equation for drdt\frac{dr}{dt} by differentiating the volume of a sphere with respect to time and then substituting the given radius to find the rate of change of the radius.
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Solution by Steps
step 1
Given the differential equation ddt(4πr2)=8πrdrdt\frac{d}{dt}(4\pi r^2) = 8\pi r \frac{dr}{dt}, we need to solve for dSdt\frac{dS}{dt} when r=5r=5 and drdt=150\frac{dr}{dt}=\frac{1}{50}
step 2
Differentiate 4πr24\pi r^2 with respect to tt to get 8πrdrdt8\pi r \frac{dr}{dt}
step 3
Substitute r=5r=5 and drdt=150\frac{dr}{dt}=\frac{1}{50} into the equation to solve for dSdt\frac{dS}{dt}, resulting in dSdt=8π(5)(150)\frac{dS}{dt} = 8\pi (5) \left(\frac{1}{50}\right)
step 4
Calculate dSdt\frac{dS}{dt} to get dSdt=8π⋅5⋅150\frac{dS}{dt} = 8\pi \cdot 5 \cdot \frac{1}{50}
step 5
Simplify the equation to find dSdt\frac{dS}{dt}, which gives dSdt=8π⋅550\frac{dS}{dt} = \frac{8\pi \cdot 5}{50}
step 6
Calculate dSdt\frac{dS}{dt} to get dSdt=8π10=4π5\frac{dS}{dt} = \frac{8\pi}{10} = \frac{4\pi}{5}
Answer
dSdt=4π5\frac{dS}{dt} = \frac{4\pi}{5} when r=5r=5 and drdt=150\frac{dr}{dt}=\frac{1}{50}
Key Concept
Solving for the rate of change of surface area
Explanation
We found the rate of change of the surface area of a sphere by differentiating the surface area formula with respect to time and then substituting the given radius and rate of change of the radius.
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Solution by Steps
step 1
Calculate the value of 8π⋅5⋅1508\pi \cdot 5 \cdot \frac{1}{50}
step 2
Simplify the expression to get 8π⋅550\frac{8\pi \cdot 5}{50}
step 3
Further simplify to get 8π10\frac{8\pi}{10} which is equal to 4π5\frac{4\pi}{5}
Answer
4π5\frac{4\pi}{5}
Key Concept
Multiplication and simplification of fractions
Explanation
We multiplied and simplified the given numbers and pi to find the final value.
Question ONE (Total: 8 marks; 2 marks each) Suppose Tiger Bank's initial balance sheet is as follows (in millions). The current required reserve ratio is ONLY 10%10 \%. \begin{tabular}{|l|l|l|l|} \hline Assets & Liabilities \\ \hline Reserves & $600\$ 600 & Deposit & $5,000\$ 5,000 \\ \hline Loans & $2,200\$ 2,200 & Equity & $300\$ 300 \\ \hline Securities & $2,500\$ 2,500 & & \\ \hline TOTAL & $5,300\mathbf{\$ 5 , 3 0 0} & TOTAL & $5,300\mathbf{\$ 5 , 3 0 0} \\ \hline \end{tabular} a) What is the bank's required reserve? b) Tiger Bank runs into a huge withdrawal of $500M\$ 500 \mathrm{M}. Describe an option that is available for the bank to mitigate this problem based on Purchase Liquidity Management. Show this balance sheet, assume the bank only keeps the minimum required reserve. c) Tiger Bank runs into a huge withdrawal of $500M\$ 500 \mathrm{M}. Show the balance sheet if the bank is to liquidate some securities at 10%10 \% discount to meet the withdrawal, assume the bank only keeps the minimum required reserve. d) Banks can minimize losses by adding restrictive covenant to the loan agreements. State any TWO different types of covenants that can reduce moral hazard problems.
Generated Graph
Solution by Steps
step 1
To find the bank's required reserve, we multiply the total deposits by the required reserve ratio
step 2
The required reserve ratio is 10% 10\% or 0.10 0.10
step 3
The total deposits are $5,000M \$5,000M
step 4
Calculating the required reserve: $5,000M×0.10=$500M \$5,000M \times 0.10 = \$500M
Answer
The bank's required reserve is \$500M.
Key Concept
Required Reserve Calculation
Explanation
The required reserve is calculated by multiplying the total deposits by the reserve ratio.
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step 1
To mitigate a huge withdrawal, the bank can use Purchase Liquidity Management by borrowing funds or selling assets
step 2
Assuming the bank only keeps the minimum required reserve, it needs to cover a withdrawal of $500M \$500M
step 3
The bank can borrow $500M \$500M or sell assets to maintain the required reserves and cover the withdrawal
Answer
The bank can borrow funds or sell assets to cover the withdrawal and maintain the required reserves.
Key Concept
Purchase Liquidity Management
Explanation
The bank can manage liquidity by borrowing or selling assets to meet withdrawal demands while maintaining required reserves.
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step 1
To meet the withdrawal by liquidating securities, calculate the amount of securities to be sold at a 10% discount
step 2
The bank needs to cover $500M \$500M and will receive only 90% of the value of the securities sold
step 3
Calculate the face value of securities to be sold: $500M0.90≈$555.56M \frac{\$500M}{0.90} \approx \$555.56M
step 4
The bank will liquidate $555.56M \$555.56M of securities at a 10% discount to receive $500M \$500M
step 5
Update the balance sheet by reducing the securities by $555.56M \$555.56M and the deposits by $500M \$500M
Answer
The bank will liquidate approximately \$555.56M of securities at a 10% discount to receive \$500M.
Key Concept
Liquidation of Securities at a Discount
Explanation
To meet withdrawal demands, the bank can liquidate securities at a discount, calculating the face value needed to cover the withdrawal amount.
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step 1
Restrictive covenants in loan agreements can reduce moral hazard by imposing conditions on borrowers
step 2
Two types of covenants that can reduce moral hazard are affirmative covenants and negative covenants
step 3
Affirmative covenants require the borrower to perform certain actions, while negative covenants restrict the borrower from certain activities
Answer
Two types of covenants that can reduce moral hazard are affirmative covenants and negative covenants.
Key Concept
Restrictive Covenants in Loan Agreements
Explanation
Restrictive covenants can reduce moral hazard by requiring borrowers to engage in or refrain from specific actions, thereby protecting the lender's interests.
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