What Annual Interest Rate is Equivalent to 7% Per Year, Compounded Semiannually?

Explanation

Questions of this type are illustrating the concept of an Effective Interest Rate, which is a rate compounded annually that has the same effect as a rate compounded more often than one time a year. As such, a depositor or a creditor is indifferent between them, since they have the same effect. To solve this question, make any deposit and see how much is in the account after one year. The ratio of the ending FV to the beginning PV will indicate the annual rate earned. On the BAII Plus, press 2 N, 7 divide 2 = I/Y, 100 PV, 0 PMT, CPT FV. On the HP12C, press 2 n, 7 ENTER 2 divide i, 100 PV, 0 PMT, FV. The number displayed will be 107.12. In other words, after one year, $100 has become $107.12. An interest rate of 7.12%, compounded annually, would cause a $100 deposit to become $107.12 in one year. Choosing an initial deposit of $100 helps a great deal in these situations. Make sure the BAII Plus has the value of P/Y set to 1.