Question

Fine-Tuned Savings Association finds that it can attract the following amounts of deposits if it offers new depositors and those rolling over their maturing CDs at the interest rates indicated below: Expected Volume of New Deposits Rate of Interest Offered Depositors $10 million 2.00% 15 million 2.25 20 million 2.50 24 million 2.75 26 million 3.00 Management anticipates being able to invest any new deposits raised in loans yielding 5.50 percent. How far should this thrift institution go in raising its deposit interest rate in order to maximize total profits (excluding interest costs)?

With explanations please

Answer 1

To answer this question, we have all the data required to compute the profit. The company raises funds through loan deposits and invests these funds to earn income. The amount that can be raised by way of loan deposits and the rate of interest earned on investment of these amount is given.

We can see here, as the company go on increasing the interest rate from 2% to till 3%, the amount raised is also increasing. However, the interest the company is going to earn by utilising these loan deposits is constant. The total interest on investment that remains with the company after payment of interest on loan deposits is the actual profit of the company. This is calculated in the form of a table and the image of the same is attached here for your reference -

From the above table, it is clear that the profit is maximum when company raises $ 24 million at 2.75%. The maximum profit for the company is $ 0.66 million.(i.e., $ 6,60,000).

Hence, it is advisable for the company to go on increasing its deposit interest rate till 2.75% at which the profit of the company is maximum. If it further increases the interest rate, even though it could raise additional funds, the total profit falls down as shown in the above image.