A bank expects to raise $30 million in new money if it pays a deposit rate of 7%,$60 million in new money if it pays a deposit rate of 7.5%,$80 million in new money if it pays a deposit rate of 8%,and it can raise $100 million in new money if it pays a deposit rate of 8.5%.The bank expects to earn 9% on all money that it receives in new deposits.What is the marginal cost of deposits if this bank raises its deposit rate from 7.5% to 8%?

Question

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The marginal cost of deposits when raising the deposit rate from 7.5% to 8% is calculated by considering the additional cost to the bank for the extra money raised and the additional interest it has to pay. The bank raises an additional $20 million ($80 million - $60 million) by increasing the deposit rate by 0.5% (from 7.5% to 8%). The additional interest cost on this $20 million is 0.5% (the increase in the deposit rate), which equals $0.1 million ($20 million * 0.5%). However, the bank earns 9% on all new deposits, including the additional $20 million. The net cost to the bank is the difference between what it pays on the additional deposits (8%) and what it earns (9%), which is -1%. Therefore, the marginal cost is not just the additional interest paid but also includes the consideration of the earnings on the new deposits. The correct calculation involves finding the additional cost of raising funds and the net return on those funds.

A Bank Expects to Raise $30 Million in New Money