Suppose that, at time t = 0 (now), there are 100 depositors (householders) deposit $1,000 each to a fictitious bank, call it OUR bank. The deposits have one-year maturity and the bank pays 3% interest rate, annually compounded. The OUR bank pools all the deposits, and lends $50,000 each to two corporations. The loan terms are following: Maturity = 6 years, and Interest rate is 5% simple interest; it is the Interest ONLY loan for FIRST FOUR YEARS, therefore, during the first four-year of the loan only interest needs to be paid. After that, the principal amount has to be repaid in two equal installments at the end of year 5 and year 6. In addition, the owners have put $2,000 of equity capital. For exposition, we will make additional assumptions: No taxes, no dividend payments, no time value of money (bank will not reinvest the interest income). The OUR bank will cease to exist after six years.

Problem 1

Make the following three assumptions:

(1) Short-term (one-year) interest rate remains at 3% per annum for the next six years.

(2) Both the borrowers do not default on their loan obligations.

(3) All depositors renew their one-year deposits throughout the six years, but consume the interest payments. In other words, no principal withdrawals and no addition of principal from the depositors for the next six years.

What will be the equity position of the bank at the end of six years, t = 6 year, that also includes the initial owners equity?