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April 4th, 2018, 03:44 AM   #1
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The question of algebra

Hello, who could help me with the question of algebra and give formulas on which it is considered? The question also posted on the homework help site and mathematical forums, but the answer was never received. Stuck specifically...
To purchase studio space, on April 3, 2025 a pianist takes out a 30-year loan of \$120,000 at an annual interest rate of 11%. The first monthly payment is to be made on May 3, 2025; the final payment is scheduled to be made April 3, 2055. The monthly payment is \$1,142.79. [Note: If you use the table, you’ll get that the monthly payment is \$1,142.40, but the table produces an approximation. \$1,142.79 is the precise payment.

a) Calculate the total interest charged over the course of the loan, assuming that nothing but the standard payment is made each month.
b) How much will she owe immediately after making the payment on June 3, 2025? (= the second payment) Round appropriately to the nearest penny.
c) Suppose that as part of that June 3, 2025 payment she pays an extra \$300 as an overpayment. Calculate the dollar amount of interest which this saves in the future. Round your answer down to the nearest \$10.

Last edited by skipjack; April 4th, 2018 at 01:47 PM.
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April 4th, 2018, 07:55 PM   #2
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(a) As the repayments total 360 × \$1,142.79 = \$411,404.40, the total interest charged is \$291,404.40.

How is the interest calculated?
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April 4th, 2018, 09:33 PM   #3
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Part b)
May 3/25: 120,000.00 * (1 + .11/12) - 1,142.79 = 119,957.21
Jun 3/25: your turn!

Part c)
300 * (1 + .11/12)^358 - 300 = ?
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April 5th, 2018, 01:10 AM   #4
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I recently saw this issue .... Actually, I think the answer will be this:
Here is an amortization schedule of your loan. All the info you need is there. Look at top right-hand corner and you will see total payments, total interest, monthly payment.....etc.
If you paid \$300 off the principal after the 2nd payment, that means you will save interest on it for 358 months. So, \$300 x 1.009166667^358 =\$7,867.53 - \$300 =\$7,567.53 - this is the amount of interest you will have saved on a \$300 payment over the remaining 358 months.
Thanks from ScottyBlack228

Last edited by greg1313; April 5th, 2018 at 01:21 AM.
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April 5th, 2018, 01:47 AM   #5
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I remembered this question a couple of days ago on the forum freemathhelp and the spam site everywhere and immediately you need to ask questions, do not you?
(not advertising, find out the truth)

Last edited by greg1313; April 5th, 2018 at 02:35 AM.
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April 5th, 2018, 01:49 AM   #6
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Yes indeed you are right, I had to get an answer urgently and I used all resources.
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April 5th, 2018, 02:37 AM   #7
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If all the repayments (including the final one) are equal, the interest rate isn't precisely 11%. Also, assumptions need to be made as to whether interest is rounded, etc.
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April 5th, 2018, 04:07 AM   #8
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Skip, why is he in the "banned camp"? Not that I care
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April 5th, 2018, 04:23 AM   #9
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Denis

This cynical old man has a suspicion that all those edited posts contained url's of for-pay sites.
Thanks from Denis and topsquark
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April 5th, 2018, 05:04 AM   #10
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Thanks Jeff...and probably the infamous studydaddy site...
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