A bank makes four kinds of loans to its personal customers
Ask Expert

Be Prepared For The Toughest Questions

Practice Problems

A bank makes four kinds of loans to its personal customers

3. Financial planning: A bank makes four kinds of loans to its personal customers. These loans 10 Marks yield the following annual interest rates to the bank: 

• First mortgage 15% 

• Second mortgage 20% 

• Home improvement 20% 

• Personal overdraft 10% 

The bank has a maximum foreseeable lending capability of $350 million and is further constrained by the following policies:

1. first mortgages must be at least 55% of all mortgages issued and at least 25% of all loans issued (in $ terms) 

2. second mortgages cannot exceed 25% of all loans issued (in $ terms) 

3. to avoid public displeasure and the introduction of a new windfall tax the average interest rate on all loans must not exceed 16%.

Formulate the bank’s loan problem as an LP problem so as to maximize interest income while satisfying the policy limitations. Note here that these policy conditions, while potentially limiting the profit that the bank can make, also limit its exposure to risk in a particular area. It is a fundamental principle of risk reduction that risk is reduced by spreading money (appropriately) across different areas. 

Hint
Mathematicsobjective -> max : 15%x1 + 20%x2 + 20%x3 + 10%x4constraints -> x1 + x2 + x3 + x4 <= 350 x1 >= 0.55(x1 + x2) x1 >= 0.25(x1 + x2 + x3 + x4) x2 <= 0.25(x1 + x2 + x3 + x4) 0.14x1 + 0.20x2 + 0.20x3 + 0.10x4 <= 0.15(x1 + x2 + x3 + x4) x1 >= 0 x2 >= 0 x3 >= 0 x4 >= 0 ...

Know the process

Students succeed in their courses by connecting and communicating with
an expert until they receive help on their questions

1
img

Submit Question

Post project within your desired price and deadline.

2
img

Tutor Is Assigned

A quality expert with the ability to solve your project will be assigned.

3
img

Receive Help

Check order history for updates. An email as a notification will be sent.

img
Unable to find what you’re looking for?

Consult our trusted tutors.

Developed by Versioning Solutions.