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# Finding monthly payment

#### JamesVU2000

##### Member
Calculate a fixed rate mortgage payment, and its principal and interest components.
As the name suggests, fixed rate mortgage carries constant interest rate throughout its lifetime with level payments. The monthly repayment amount for a fixed rate mortgage is computed such that its present value when discounted at the monthly compounded mortgage (fixed) rate equals the original amount of the loan borrowed by the obligor. The formula can be depicted mathematically as:
1
tenure of the loan in years.
For example: Calculate fixed rate mortgage payment with following parameters:
 Principal Amount: (0) = $100,000  Rate of Interest: = 4% per annum  Loan Tenure: = 30 Years How do find the monthly payment with calculator? I don’t understand how to input the formula. Thanks James #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @JamesVU2000 Here are keystrokes, roughly left to right with TVM keys on my TI BA II+. Notice we need to multiply 30 years by 12, and consistently divide 4 (%) rate by 12, to deal in periods of one month. Also, the future value (FV) is zero, so that the loan fully amortizes. "#" just means "my comment for you." Hope this helps: 360 [N] # diplay: N = 360 4 ÷ 12 = [I/Y] # display: I/Y = 0.3333 100000 [+/-] [PV] # display: PV = -100,000.0000 0 [FV] # display: FV = 0.0000 [CPT] [PMT] # display answer: PMT= 477.4153 #### JamesVU2000 ##### Member Thanks for for the help, David. What do you recommend for help with calculator? I feel like the exam relies on it a lot and you need to know it well. #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Sure @JamesVU2000 I like the actual manual https://www.bionicturtle.com/forum/resources/ti-ba-ii-pro-calculator-instructions.110/ ... I do think we (BT) should record some videos with basic help. It's true that for the exam you do need to know it well. It's may an underappreciated skill, to be fluent with the calculator which is important when time is short. Nicole and I try to add some calculator resources to the schedule (we have a new person helping with content and it looks like he might be good/great/excellent so we should have the capacity ...). Thanks, #### JamesVU2000 ##### Member 1. Suppose a lender quotes the interest rate on a$1,000 loan as 9.0% per annum with continuous compounding but the interest is actually paid monthly. What are the monthly interest payments?
a) $7.47 b)$7.50 c) $7.53 d)$7.59. Should I beable to do this with a calculator? I can’t figure out how to enter it in ti. I’m sorry for bothering you and appreciate your help or anyone else’s

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @JamesVU2000 No problem, I'm here working anyway (and it's super quick for me)! In this case, you need to translate the 9.0% continuous rate into its monthly (discrete) equivalent with R_m = m*[exp(R_m/m)-1], where here m = 12 periods per year so R_m = 12*[exp(0.09/12)-1] = 9.033835%. Per calculator: .09 ÷ 12 = .0075 [2nd][e^x] - 1 * 1000 = 7.5282. So if you pay this amount at the end of each month, it will equal $1,000*exp(9%*1) =$1,094.1743 - $1000 =$94.1743 in cumulative interest, is the amount of interest paid continuously at 9.0% or 9.033835% per annum with monthly compound frequency. Hope that helps!

#### JamesVU2000

##### Member
thanks for the help. How do enter 1000*exp(9%*1)? thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
I like to go inside out, so I do this: .09 × 1 = [2nd] [e^x] × 1000 = ... display: 1,094.1743
... but you can go left to right: 1000 × (.09 × 1) [2nd] [e^x] = ... 1,094.1743

#### JamesVU2000

##### Member
in hull example for bionomial tree f= 5-3.5*exp(-1%)=1.53483. Do I subtract 5-3.5= 1.5 then [2nd][e^x] -1%? if anyone else besides david can answer this I would appreciate it. I cant find any explanations with the manual.