My Math Forum finance: monthly, balance, and interest
 User Name Remember Me? Password

 Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 April 4th, 2014, 12:29 AM #1 Newbie   Joined: Apr 2014 From: mars Posts: 7 Thanks: 2 finance: monthly, balance, and interest tim takes out a 15-year loan of the amount $300,000. The annual interest rate is 4% , compounded monthly. Answer the following questions. i What will Bob's monthly payment be? ii: Ten years into his repayment program, what will tim's balance owed be? iii: After 15 years, how much will Bob have spent on interest? please help me. DX Last edited by looni; April 4th, 2014 at 12:31 AM.  April 4th, 2014, 12:46 AM #2 Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs If you have not been given a formula for the monthly payment amount, this can be derived as follows: Let$P$= monthly payment,$A$= amount borrowed,$i$= monthly interest rate, and$n$= the number of payments. Also, let$D_n$be the debt amount after payment$n$. Consider the recursion: (1)$\displaystyle D_{n}=(1+i)D_{n-1}-P$(2)$\displaystyle D_{n+1}=(1+i)D_{n}-P$Subtracting (1) from (2) yields the homogeneous recursion:$\displaystyle D_{n+1}=(2+i)D_{n}-(1+i)D_{n-1}$whose associated auxiliary equation is:$\displaystyle r^2-(2+i)r+(1+i)=0\displaystyle (r-(1+i))(r-1)=0$Thus, the closed-form for our recursion is:$\displaystyle D_n=k_1(1+i)^n+k_2$Using initial values, we may determine the coefficients$k_i$:$\displaystyle D_0=k_1+k_2=A\displaystyle D_1=k_1(1+i)+k_2=(1+i)A-P$Solving this system, we find:$\displaystyle k_1=\frac{Ai-P}{i},\,k_2=\frac{P}{i}$and so we have:$\displaystyle D_n=\left(\frac{Ai-P}{i} \right)(1+i)^n+\left(\frac{P}{i} \right)=\frac{(Ai-P)(1+i)^n+P}{i}$Now, equating this to zero, we can solve for$P$:$\displaystyle \frac{(Ai-P)(1+i)^n+P}{i}=0\displaystyle (Ai-P)(1+i)^n+P=0\displaystyle (P-Ai)(1+i)^n=P\displaystyle P\left((1+i)^n-1 \right)=Ai(1+i)^n\displaystyle P=\frac{Ai(1+i)^n}{(1+i)^n-1}\displaystyle P=\frac{Ai}{1-(1+i)^{-n}}$Now, you can plug in the given values to get$P$and use other formulas in the above to answer the remaining questions as well. April 6th, 2014, 09:20 AM #3 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 Quote:  Originally Posted by looni tim takes out a 15-year loan of the amount$300,000. The annual interest rate is 4% , compounded monthly. Answer the following questions. i What will Bob's monthly payment be? ii: Ten years into his repayment program, what will tim's balance owed be? iii: After 15 years, how much will Bob have spent on interest? please help me. DX
1: Mark gave you formula
2: That'll the PV of the payment at month 120 (n = 60)
3: payment * 180 - 300000
OK?

April 6th, 2014, 12:20 PM   #4
Math Team

Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,950
Thanks: 987

Quote:
 Originally Posted by Denis 2: That'll the PV of the payment at month 120 (n = 60)
Clarification:
That'll the PV of the payments left following month 120 (n = 60)

Can't edit no more?!

April 6th, 2014, 10:08 PM   #5
Newbie

Joined: Apr 2014
From: mars

Posts: 7
Thanks: 2

Quote:
 Originally Posted by Denis Clarification: That'll the PV of the payments left following month 120 (n = 60) Can't edit no more?!

i got it thanks! ^^

 May 22nd, 2015, 04:22 AM #6 Newbie   Joined: May 2015 From: usa Posts: 6 Thanks: 0 Math Focus: trigonometry Hello, This Loan Payment Calculator computes an estimate of the measure of your monthly credit instalments and the yearly income needed to manage them without too much financial trouble. This loan calculator expects that the interest rate stays consistent for the duration of the life of the credit. Thanks Ailsajohn@
May 22nd, 2015, 10:40 PM   #7
Member

Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

Quote:
 Originally Posted by looni tim takes out a 15-year loan of the amount \$300,000. The annual interest rate is 4% , compounded monthly. Answer the following questions. i What will Bob's monthly payment be? ii: Ten years into his repayment program, what will tim's balance owed be? iii: After 15 years, how much will Bob have spent on interest? please help me. DX
Bob's payment will be zero as it was Tim who took out the loan and not Bob unless Tim stole Bob's identity in which case now Bob has a dilemma

 Tags balance, finanace, finance, interest, monthly

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post looni Economics 3 April 6th, 2014 10:12 PM FlintheartGlomgold Calculus 3 April 4th, 2014 12:31 AM proglote Algebra 2 May 10th, 2011 06:45 PM AmericanPerson Algebra 4 November 11th, 2009 02:23 PM linux44 Calculus 1 February 1st, 2008 08:41 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top