Question

A major property developer is concerned about lack of sales due to local economic conditions. To ensure that his condos are occupied, he offers a lease-to-purchase program in which, if people sign a lease by the end of March, they will not have to start making payments until March of the following year. The purchase price of the condo is $191,000. Payments of $1065.67 will be required at the beginning of each month over a 25-year amortization period. If interest is7.34 % compounded semi-annually during the first year, what is the semi-annually compounded interest rate during the payment period?

ANSWER: The interest rate during the payment period is compounded 3.90% semi-annually. (Round the final answer to two decimal places. Round all intermediate values to six decimal places as needed.)

NOTE*: i would like to know how to get to that answer through a financial calculator in BGN MODE. If it is not possible to calculate through financial calculator then formulas are okay too! (Simple annuity)

Answer 1

The purchase price is 191000 You will start to make payment from the next year, beginning of each month We first need to calculate the value of purchase price at time period 1, because that is when you start to make the payments 191,000.00 At time period 1 the 191000*(1+0.0734/2)^2 205,276.66 Use the financial calculator, set it to begin mode Present value 205,276.66 Number of payments 25*12 = Periodic payment 1065.67 Calculate the value of monthly interest rate by using the calculator Monthly Interest = 0.322695 Nominal annual interest rate = 0.322695*12 3.87234 The interest rate compounded semiannualy would be = (1+0.0387/2)^2-1 0.0390 3.90%