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Deposit Valuation


A deposit is an amount of money, whether in the form of cash, checks, or drafts, that is placed with a bank (or a similar financial institution) for credit to a customer’s account. A standard unit deposit at time T pays at maturity M an amount equal to:

DTT(Unit) = 1+ α LT [T, M]

where α is the accrual factor, and L is interest rate.

Since there are no further payments other than the initial deposit and the final repayment, these two cashflows must have the same value at time T. Therefore, if follows that:

DTT = DTT(Unit) × DTS ⇒ DTM = DTT / DTT(Unit) ⇒ DTM = DTT / DTT(Unit)

DTM = DTT / (1+ α LT [T, M]) ⇒ LT [T, M] = (DTT – DTM )/ α DTM

This means the value of of a deposit placed over a period of [T, M] is the difference between its values at deposit time and withdrawal time divided by its terminal value adjusted with a corresponding accrual factor.



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