Question 1193770: Find the cash price of a property if it is bought for $150,000 down payment and payments of $15,000 at the end of every 3 months for 7 years if money is worth 10% compounded quarterly.
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! **1. Calculate the Present Value of the Quarterly Payments:**
* **Quarterly Interest Rate:** 10% annual interest / 4 quarters per year = 2.5% per quarter (0.025)
* **Number of Payments:** 7 years * 4 quarters/year = 28 payments
* **Present Value of an Ordinary Annuity Formula:**
Present Value = Payment * [(1 - (1 + r)^-n) / r]
Where:
* Payment = $15,000
* r = Quarterly interest rate (0.025)
* n = Number of payments (28)
* **Calculate:**
Present Value = $15,000 * [(1 - (1 + 0.025)^-28) / 0.025]
Present Value ≈ $15,000 * 19.9635
Present Value ≈ $299,452.50
**2. Calculate the Cash Price of the Property**
* Cash Price = Down Payment + Present Value of Payments
* Cash Price = $150,000 + $299,452.50
* Cash Price = $449,452.50
**Therefore, the cash price of the property is approximately $449,452.50.**
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