Mathematics OF Finance MMW PDF

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Exercises: (Simple Interest-Simple Discount-Promissory Note) 1. A small business owner Borrowed Php8,500.00 at 9% for 18 months. How much interest will be repaid upon maturity of the loan? P = 8500; r = 9% or 0.09; I = Prt = (8500)(0.09)(1.5) = P1147.5

t = 18

2. On May 10X. Victoria borrowed Php25,000.00 from the bank at 18% interest. What is the interest charge on the loan if she will pay her obligation on August 8? P = 25000; r = 18% or 0.18; I = Prt = (25000)(0.18)(0.24) = P1080

t = 90

3. Discount Php1,500.00 for three years at 6% simple interest? F = 1500; 𝐹 P= =

r = 6% or 0.06;

t=3

(1+𝑟𝑡) 1500 [1+(0.06)(3)]

P = P1271.19 4. If money is worth 6 %, find the present value on Php2,800.00 due in 5 years? F = 2800; P= =

t = 5;

r = 6.5

𝐹 1+𝑟𝑡 2800 1+(0.065)(5)

P = P2113.21 5. If Php5,255.60 is the present value of Php6,350.00 which due at the end of 10 months, find the simple interest rate? F = 6350;

P = 5255.60;

t = 10 months

r= =

𝐹−𝑃 𝑃𝑡 6350 – 5255.60 (5255.60)(0.83)

= 0.25 or 25% 6. How many months will it take for Php10,000.00 to earn Php890.00 if it is invested at 8% simple interest? P = 10000; r = 8% or 0.08; t= =

I = 890

𝐼 𝑃𝑟

890

(10000)(0.08)

t = 1.1125 (13 months) 7. Find the interest and amount on Php9,700.00 at 4 % for three months. P = 9700; r = 4.5%; t = 0.25 I = Prt = (9700)(4.5)(0.25) I = P10912.5 8. Accumulate Php9,400.00 for 45 days at 5 %. P = 9400; r = 5.75; t = 45 F = P(1+rt) = 9400[1+(5.75)(0.12)] F = P9464.86 9. At what rate must Php7,900.00 be invested to accumulate to Php10,600.00 in 120 days? I = 10600; P = 7900; t = 120 𝐼 r= =

𝑃𝑡 10600

7900(0.32)

r = 4.19% 10. Find the present value of Php4,700.00 due in seven months at 7% discount rate.

F = 4700; P= =

t = 7 months;

r = 9% or 0.09

𝐹 1+𝑟𝑡 4700 1+(0.09)(0.58)

P = P4466.83 11. Discount Php3,080.00 for 85 days at a discount rate of 5 %. F = 3080; P= =

r = 5.75%; t = 85 days

𝐹 (1+𝑟𝑡) 3080 1+(0.0575)(0.23)

P = P3039.80 12. Mrs. Tabachoy invested Php12,300.00 at 13% for 5years. What is the equivalent discount rate for this transaction? r = 13% or 0.13; 𝑟 d= =

t = 5 years

1+𝑟𝑡 0.13

1+(0.13)(5)

= 0.08 or 8%

13. Find the discount rate which is equivalent to the simple interest rate of 12% in accumulating or discounting money for six months. r = 12% or 0.12; 𝑟 d= =

t = 6 months

1+𝑟𝑡 0.12

1+(0.12)(0.5)

= 0.11 or 11% 14. Raja Wholesales receives a Php50,000.00 note for goods sold to a retailer. The note matures in three months and bears a 14% simple interest rate. One month later the wholesaler find herself short of cash and sells her note to a bank at 15% discount rate. P = 50000; r = 14% or 0.14; t = 1 month

a. What is the maturity value of the note? P = 50000; r = 14% or 0.14; F = P (1+rt) F = 50000 [1+(0.14)(0.25)] F = P51750

t=

90 360

b. What is the proceeds which Raja received? F = P51750;

d = 15% or 0.15; t =

1 12

P = F(1 – dt) P = 51750[1 – (0.15)(0.083)] P = 51105.71 Php 51105.71 – Php 50000 = Php 1195.71 proceeds of Raja c. How much gross profit would the bank make if it keeps the note to maturity? F = P51750;

d = 15% or 0.15;

t=

90 360

P = F (1 – dt) P = 51750 [1 – (0.15)(0.25)] P = 49809.38 Php 51750 – Php 49809.38 = 1940.62 bank’s profit 15. On September 12, 2003 Ica-Mataba draws a note to the order of Aquila-dragon Enterprises to pay Php40,000.00 without interest at the end of four months. Find the proceeds for Aquila-dragon enterprises if the note is discounted for her at 16% on October 18, 2003 by FAT bank. Maturity Date - January 13, 2004 Term of Discount: Ordinal Day of January 13 Ordinal Day of October 18 Term of Discount

-13 -291 278 days

P = 40000;

r=0

t = 278 days;

F = P (1 + rt) = 40000 [1 + (0)(0.77)] = Php 40000

F = 40000; d = 16% or 0.16;

t = 278 days

P = F (1 – dt) = 40000 [(1 – (0.16)(0.77)] = Php 35072 Php 40000 – Php 35072 = Php 4928 proceeds of Aquila-dragon enterprises 16. A four-month note whose face value is Php5,600.00 bears interest at 7%. The note is discounted two months before maturity at a bank whose discount rate is 4 %. Find the proceeds. P = 5600; 𝑃 F= 1−𝑑𝑡

=

d = 4.75%;

5600

1−(0.0475)(0.17)

F = P5645.73 P= =

𝐹 1+𝑟𝑡 5645.73 1+(0.07)(0.17)

P = P5579.34

t = 2 months;

r = 7% or 0.07...