SOLUTION: A farmer wants to sell his small farm to a real estate agent. Determine the total amount the agent can deposit now, at 3% compounded quarterly, so that it is enough to pay $ 750,00
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Question 1177373: A farmer wants to sell his small farm to a real estate agent. Determine the total amount the agent can deposit now, at 3% compounded quarterly, so that it is enough to pay $ 750,000 within 3 years.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down how to calculate the present value needed.
**Understanding the Problem**
We need to find out how much money the real estate agent needs to deposit *now* so that it grows to $750,000 in 3 years, with a 3% annual interest rate compounded quarterly.
**Calculations**
1. **Interest Rate per Quarter:**
* Annual interest rate: 3% = 0.03
* Quarterly interest rate: 0.03 / 4 = 0.0075
2. **Number of Quarters:**
* Number of years: 3
* Number of quarters: 3 years * 4 quarters/year = 12 quarters
3. **Present Value Formula:**
* Present Value (PV) = Future Value (FV) / (1 + interest rate)^number of periods
* PV = FV / (1 + r)^n
4. **Plug in the Values:**
* PV = $750,000 / (1 + 0.0075)^12
* PV = $750,000 / (1.0075)^12
* PV = $750,000 / 1.0934433068
* PV ≈ $685,678.62
**Answer**
The real estate agent should deposit approximately $685,678.62 now.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
A farmer wants to sell his small farm to a real estate agent.
Determine the total amount the agent can deposit now, at 3% compounded quarterly,
so that it is enough to pay $ 750,000 3 years.
~~~~~~~~~~~~~~~~~~~~~~~~~
The problem's formulation, given in the post, is/was incorrect.
I edited it in order for it would make sense.
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