Question 1179711: Determine the periodic payments on the given loan or mortgage.
$5,000,000 borrowed at 7% for 30 years, with quarterly payments
PMT =
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the quarterly payment for the loan:
**1. Given Information:**
* Principal (P): $5,000,000
* Annual interest rate (r): 7% or 0.07
* Loan term (t): 30 years
* Compounding periods per year (n): 4 (quarterly)
**2. Calculate the Quarterly Interest Rate (i):**
* i = r / n = 0.07 / 4 = 0.0175
**3. Calculate the Total Number of Payments (N):**
* N = n * t = 4 * 30 = 120
**4. Use the Loan Payment Formula:**
PMT = P * [i * (1 + i)^N] / [(1 + i)^N - 1]
Where:
* PMT = periodic payment
* P = principal
* i = interest rate per period
* N = total number of payments
**5. Plug in the Values:**
PMT = 5000000 * [0.0175 * (1 + 0.0175)^120] / [(1 + 0.0175)^120 - 1]
PMT = 5000000 * [0.0175 * (1.0175)^120] / [(1.0175)^120 - 1]
**6. Calculate (1.0175)^120:**
(1.0175)^120 ≈ 7.612255
**7. Substitute and Solve:**
PMT = 5000000 * [0.0175 * 7.612255] / [7.612255 - 1]
PMT = 5000000 * [0.1332144625] / [6.612255]
PMT = 5000000 * 0.0201465
PMT = 100732.5
**Answer:**
The quarterly payment (PMT) is approximately $100,732.50.
Answer by ikleyn(52817)  (Show Source):
You can put this solution on YOUR website! .
Determine the periodic payments on the given loan or mortgage.
$5,000,000 borrowed at 7% for 30 years, with quarterly payments
~~~~~~~~~~~~~~~~~~~~~~~~~
I used the same formulas as in the post by @CPhill.
I calculated using MS Excel and Google spreadsheets.
My final result is different from that by @CPhill.
Here's how to calculate the quarterly payment for the loan:
**1. Given Information:**
* Principal (P): $5,000,000
* Annual interest rate (r): 7% or 0.07
* Loan term (t): 30 years
* Compounding periods per year (n): 4 (quarterly)
**2. Calculate the Quarterly Interest Rate (i):**
* i = r / n = 0.07 / 4 = 0.0175
**3. Calculate the Total Number of Payments (N):**
* N = n * t = 4 * 30 = 120
**4. Use the Loan Payment Formula:**
PMT = P * (i * (1 + i)^N) / ((1 + i)^N - 1)
Where:
* PMT = periodic payment
* P = principal
* i = interest rate per period
* N = total number of payments
**5. Plug in the Values:**
PMT = 5000000 * (0.0175 * (1 + 0.0175)^120) / ((1 + 0.0175)^120 - 1)
PMT = 5000000 * (0.0175 * (1.0175)^120) / ((1.0175)^120 - 1)
PMT = 99965.84. <<<---=== obtained from MS Excel and confirmed by Google spreadsheet.
**Answer:**
The quarterly payment (PMT) is $99,965.84.
Solved.
My answer is different from that by @CPhill.
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