Explanation:
| Funds Raised | Average Rate Paid | Total Interest | Marginal Cost | Change in Total Cost | Expected Revenue | Difference Expected less Marginal | Total Additional Profit |
|---|---|---|---|---|---|---|---|
| 6,000,000 | 3.00% | 180,000 | 180,000 | 3.00% | 7.00% | 4.00% | 240,000 |
| 10,000,000 | 3.25% | 325,000 | 145,000 | 3.63% | 7.00% | 3.38% | 375,000 |
| 12,000,000 | 3.50% | 420,000 | 95,000 | 4.75% | 7.00% | 2.25% | 420,000 |
| 15,000,000 | 3.75% | 562,500 | 142,500 | 4.75% | 7.00% | 2.25% | 487,500 |
| 20,000,000 | 5.50% | 1,100,000 | 537,500 | 10.75% | 7.00% | −3.75% | 300,000 |
The calculations are as follows:
Total interest = Funds raised × Average Rate Paid
= 6,000,000 × 3.00% = 180,000
Marginal cost = Change in total cost
= New interest rates × Total funds raised at new rate
− Old interest rate × Total funds raised at old rate
= (3.25 × 10,000,000) − (3.00% × 6,000,000) = 145,000
Alternatively, marginal cost is the additional interest earned in new deposit money.
Marginal cost = 325,000 − 180,000 = 145,000
Change in Total Cost =
= = 3.00%
For the second case,
Change in Total Cost = = 3.63% and so on.
XYZ Bank should raise its deposit rate to 3.75%, attracting $15,000,000 in new deposits; because up to then, the marginal revenue rate is higher than the marginal cost rate, and total profits are also rising. At 5.50%, the marginal cost rate is higher than the marginal revenue rate, and overall profits have fallen from a high of $487,500 back down to $300,000.
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Consider the following table:
| Expected Amount of New Deposits | Rate of Interest Offered to Depositors |
|---|---|
| 6,000,000 | 3.00% |
| 10,000,000 | 3.25% |
| 12,000,000 | 3.50% |
| 15,000,000 | 3.75% |
| 20,000,000 | 5.50% |
Management hopes to invest any new deposits raised in loans yielding 7%. How far should this thrift institution go in raising its deposit interest rate to maximize total profits (excluding operational costs)?
A
0.0325
B
0.035
C
0.0375
D
0.055