Financial mathematics 111 Chapter three: Discount & Present Value

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1 Financial mathematics 111 Chapter three: Discount & Present Value Bank اسم الطالب:... رقم الطالب:... الصف:... المدرسة:... الرقم التسلسلي

القیمة المستقبلیة value: Future القیمة الحالیة value: Present تاریخ الاصدار. date: Issue تاریخ التغییر.. date: Converted تاریخ الاستحقاق date: Due الخصم Discount: بیعت... Sold: تاریخ الاستحقاق.

2 القیمة المستقبلیة value: Future القیمة الحالیة value: Present تاریخ الاصدار. date: Issue تاریخ التغییر.. date: Converted تاریخ الاستحقاق date: Due الخصم Discount: بیعت... Sold: تاریخ الاستحقاق.. date: Mature الدین... debt: A اجمالي الخصم. discount: Total عمولة.. Commission: رسوم التحصیل charge: Collection خفض استقطع. Deducted: Original value Loan Future Value Ov Fv Present value Pv Issue date converted date to cash Due date 1/1/2010 1/3/2010 1/12/2010 BD1,000 BD1,200 BD1,500 Discount = BD300 Total Discount = Discount + Commission + Collection Charge Com. = Fv x Com. Rate Coll. Charge = Fv x Coll. Rate Net Present Value = Future Value Total Discount Uploaded by: Ayman Ayyad (Danger3) 2 Prepared by T: A. JALIL ALAIWI

3 First: By Using Simple Interest: D = Fv i T P v= Fv - D Exercise 1: A Face value of a note BD1,900 matures after 120 days sold to a bank at 3.2% simple discount rate, 0.5% commission and 0.1% collection charge. Find the net present value of that note?. Uploaded by: Ayman Ayyad (Danger3) 3 Prepared by T: A. JALIL ALAIWI

4 Exercise 2: A face value of note was BD6,600 matures after one year was converted into cash at the bank, the computed rate is 6% simple discount and 0.1% commission,collection charge was 0.5% Find the following:- a- Total discount. b- Net value. Exercise 3: A promissory note of BD 2,590 has a maturity date of 16th Dec 2008 was sold on 29th May 2008.Calculate the net present value of the note if the simple discount rate 7%, commission 0.2% and the collection charge BD15? Uploaded by: Ayman Ayyad (Danger3) 4 Prepared by T: A. JALIL ALAIWI

5 Exercise 4: A loan with a future value BD8,440 with 9% simple interest matures on 8 th Oct is converted to cash at Al- Ahli bank on 15 th Jun calculate the present value & discount? Exercise 5: Find the discount and percent value for the following debts: a- BD 850 for 4 years with a simple b- BD 5,500 for 10 months with a simple interest rate 12% annually. discount rate 11.5%. C-BD 1,000 for one year and 4 months annually with a simple discount rate 7% d- $ 9250 for 90 days at 6¼% simple Uploaded by: Ayman Ayyad (Danger3) 5 Prepared by T: A. JALIL ALAIWI

6 Second: By Using Compound Interest: PV = Fv x (1+ i ) -n Using a Table 2 D = Fv - PV Find the value of the following (by using interest table) a - (1.08)-34 =. b - (1.1)-65 =... Exercise 6: A Face value of a note BD1,900 matures after 120 days sold to a bank at 3.2% annually compound interest rate, 0.5% commission and 0.1% collection charge. Find the net present value of that note?. Uploaded by: Ayman Ayyad (Danger3) 6 Prepared by T: A. JALIL ALAIWI

7 Exercise 7: A face value of note was BD6,600 matures after one year was converted into cash at the bank, the computed rate is 6% quietly and 0.1% commission,collection charge was 0.5% Find the following:- a- Total discount. b- Net value. Exercise 8: A note that will mature in 3 years was sold to a bank that uses a 5% compound interest rate.the bank deducted 0.2% as a commission and BD 25 as a collection charge. Find the total discount and present value if the face value for that note was BD 55000? Uploaded by: Ayman Ayyad (Danger3) 7 Prepared by T: A. JALIL ALAIWI

8 Exercise 9: A debt of BD9,000 dues after 2 years at compound discount rate of 7% annually - Compute the following: 1- Present value. 2- Discount. Exercise 10: Find the discount and percent value for the following debts: A-BD6050 for 4 years with a compound discount rate 10% annually compounded semi-annually. Uploaded by: Ayman Ayyad (Danger3) 8 Prepared by T: A. JALIL ALAIWI

9 b- BD3,000 for one year and 4 months with a compound discount rate 7% thirdly. Exercise 11: A note BD1,400 that will mature in 80 days was sold to a bank that uses a 5% compound discount rate. Find the present value? Exercise 12: A note BD1,400 sold to a bank before 2 years and 6 months from the maturing date at 6.5% compounded annually quarterly. Calculate the discount and present value? Uploaded by: Ayman Ayyad (Danger3) 9 Prepared by T: A. JALIL ALAIWI

10 General Exercise 1. Find the value of the following (by using interest table) a - (1.08)-34 b - (1.1) Calculate the discount and the present value of the followings: a- BD 7,860 due after 16 months at 6.5% simple interest. b- BD 8,000 due after 1.5 years at 9% annually (CI). c- BD 6,450 due after 100 days at 10%. 3. Find the present value and the discount of BD 3,200 due in 5 years if money is worth 18% monthly? 4.Find the e discount and the proceed ( present value) for a note with a future value of BD 2,400 discounted before 10 months with simple interest rate of 5% annually? 5. A note with BD 4,600 will be matured on 5/2/2008 with12% interest is converted to cash on 18/10/2009- Find the proceeds? 6. A note is matured on 18 th Feb 2009 for BD 2,000 was converted to cash on 24 th Sep 2009 at a discount rate 7%, discount rate 0.1% commission and BD as a collection fees - Find the discount and proceeds for that note? 7. Moosa Co. is a debtor of BD 40,000 to Al-Hassan Est. mature at the end of 10 years. And for clarification constraint to pay all loan now. Compute the money if it is to be paid today if the compound interest rate is 12% annually? 8. Saleem Co. bought goods from Al Montazah.He signed a note for BD 35,000 matured in 2 years If Al Montazah sold this note to a bank, with 4.5% semiannually discount rate, 0.4% commission and collection charges 0.2% - find the net present value of this note new. 9. A note for BD 8,000 will mature after 5 Years from today is sold to a bank that uses a 7% annual compound interest rate. If the bank deducted 1% as a commission. Find the net present value? 10. A note with a face value of BD 2,600 will mature after 3 Years from today is sold to a bank that uses a 6% annual compound interest rate. The bank deducted BD15 as a commission and BD72 as a collection charge. Find the net present value and total discounts. Uploaded by: Ayman Ayyad (Danger3) 10 Prepared by T: A. JALIL ALAIWI

11 Uploaded by: Ayman Ayyad (Danger3) 11 Prepared by T: A. JALIL ALAIWI

12 TABLE No.2 Equation : (PV) = FV(1+i) -N PV for one monetary unit N 0.5% 0.75% 1% 1.25% 1.5% 1.75% 2% 2.25% 2.5% TABLE No.2 Equation : (PV) = FV(1+i) -N PV for one monetary unit N 2.75% 3% 3.25% 3.5% 3.75% 4% 4.25% 4.5% Uploaded by: Ayman Ayyad (Danger3) 12 Prepared by T: A. JALIL ALAIWI

13 TABLE No.2 Equation : (PV) = FV(1+i ) -N PV for one monetary unit N 4.75% 5% 5.25% 5.5% 5.75% 6% 6.25% 6.5% Uploaded by: Ayman Ayyad (Danger3) 13 Prepared by T: A. JALIL ALAIWI

14 Uploaded by: Ayman Ayyad (Danger3) 14 Prepared by T: A. JALIL ALAIWI

15 -N TABLE No.2 Equation : (PV) = FV ( 1+i) PV for one monetary NO 6.75% 7% 7.25% 7.50% 7.75% 8% 8.25% Uploaded by: Ayman Ayyad (Danger3) 15 Prepared by T: A. JALIL ALAIWI

16 TABLE No.2 Equation : (PV) = FV ( 1+i) -N PV for one monetary NO 8.75% 9% 9.25% 9.5% 9.75% 10% 10.25% Uploaded by: Ayman Ayyad (Danger3) 16 Prepared by T: A. JALIL ALAIWI

Financial mathematics 111 Chapter two: Compound Interest

Financial mathematics 111 Chapter two: Compound Interest Bank اسم الطالب:... رقم الطالب:... الصف:... المدرسة:... الرقم التسلسلي Compound interest:.. KEY TERM INTRODUCED: Compound amount:.. Unit four and