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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 15year 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: 12,205 Thanks: 512 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) $\displaystyle D_{n}=(1+i)D_{n1}P$ (2) $\displaystyle D_{n+1}=(1+i)D_{n}P$ Subtracting (1) from (2) yields the homogeneous recursion: $\displaystyle D_{n+1}=(2+i)D_{n}(1+i)D_{n1}$ whose associated auxiliary equation is: $\displaystyle r^2(2+i)r+(1+i)=0$ $\displaystyle (r(1+i))(r1)=0$ Thus, the closedform for our recursion is: $\displaystyle D_n=k_1(1+i)^n+k_2$ Using initial values, we may determine the coefficients $k_i$: $\displaystyle D_0=k_1+k_2=A$ $\displaystyle D_1=k_1(1+i)+k_2=(1+i)AP$ Solving this system, we find: $\displaystyle k_1=\frac{AiP}{i},\,k_2=\frac{P}{i}$ and so we have: $\displaystyle D_n=\left(\frac{AiP}{i} \right)(1+i)^n+\left(\frac{P}{i} \right)=\frac{(AiP)(1+i)^n+P}{i}$ Now, equating this to zero, we can solve for $P$: $\displaystyle \frac{(AiP)(1+i)^n+P}{i}=0$ $\displaystyle (AiP)(1+i)^n+P=0$ $\displaystyle (PAi)(1+i)^n=P$ $\displaystyle P\left((1+i)^n1 \right)=Ai(1+i)^n$ $\displaystyle P=\frac{Ai(1+i)^n}{(1+i)^n1}$ $\displaystyle P=\frac{Ai}{1(1+i)^{n}}$ 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: 13,441 Thanks: 946  Quote:
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: 13,441 Thanks: 946  
April 6th, 2014, 10:08 PM  #5 
Newbie Joined: Apr 2014 From: mars Posts: 7 Thanks: 2  
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:
 

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