6. The cash price of an apartment condominium is P85,908 and can be acquired by a down payment of P50,000 and a yearly payment of P10,000 at the end of each year for 10 years star@ng at the end of 5 years from the date of purchase. If money is worth "x" percent compounded annually, what is the value of x?
Answer (1)
The value of x is 6% interest rate compounded annually.Data GivenCash price: ₱85,908Downpayment: ₱50,000Yearly payment: ₱10,000For 10 years, starting at end of 5th yearFind interest rate (x%) compounded annuallyPresent Value of Deferred AnnuityFirst, calculate the present value (PV) of the 10 yearly payments at the time of purchase. The PV of an ordinary annuity is [tex]PV = R (\frac{1-(1+x)^{-n} }{x} )[/tex].Since payments begin in year 5, we must discount the annuity back to today (year 0).R = 10000n = 10x = ?[tex]PV = R (\frac{1-(1+x)^{-n} }{x} )\\85908 = 50000 + 10000 [\frac{1-(1+x)^{-10} }{x} (1+x)^{-4} ]\\x = 6%[/tex]I used a calculator to solve it.
