1.2 Discount Interest1.2 Discount Interest

Discount Interest

1.2 Discount Interest1.2 Discount Interest

• Discount interest – a type of interest collected in advance and is taken from the amount of the loan applied for on the origin date

• Formula for discount interest Id:

€

Id = Fdt

€

F - maturity value

d - discount interest rate per year

t - term

1.2 Discount Interest1.2 Discount Interest

• The amount of the loan originally applied for would be the maturity value.

• The actual amount received by the borrower on the origin date is called the proceeds.

• Denoted by P, it is the difference between the maturity value and the discount interest.

€

P = F − Id

€

or P = F(1 − dt)

1.2 Discount Interest1.2 Discount Interest

Example. Ben borrowed Php10,000 from Mon who charged 4% discount interest. How much did Ben receive if the debt is to be repaid in 10 months?

€

P = F(1 − dt)

€

=10,000 1− (.04) 1012( )[ ]

€

P = Php9,666.67

1.2 Discount Interest1.2 Discount Interest

Derived formulas:

€

F =Iddt

€

d =IdFt

€

t =IdFd

€

F =P

1 − dt

1.2 Discount Interest1.2 Discount Interest

1. Given F = Php37,500, d = 8%, t = 5 years, find Id.

€

Id = Fdt

€

=(37,500)(.08)(5)

€

=Php4,162.50

1.2 Discount Interest1.2 Discount Interest

5. Given F = Php290,000, d = 10.35%, t = 40 months, find P.

€

P = F(1− dt)

€

=290,000 1 − (.1035) 4012( )[ ]

€

=Php189,950

1.2 Discount Interest1.2 Discount Interest

7. Given P = Php301,500, d = 8.25%, t = 4 years, find F.

€

F =P

1 − dt

€

=301,500

1− (.0825)(4)

€

=Php450,000

1.2 Discount Interest1.2 Discount Interest

9. Given F = Php4,063.49, Id = Php3,200, t = 9 years, find d.

€

d =IdFt

€

=3,200

(4,063.49)(9)

€

=8.75%

1.2 Discount Interest1.2 Discount Interest

11. Given F = Php12,000, Id = Php3,780, d = 9%, find t.

€

t =IdFd

€

=3,780

(12,000)(.09)

€

=3.5 years

1.2 Discount Interest1.2 Discount Interest

15. If you borrow Php80,000 from a lender for one year and 2 months at 3% discount interest rate, how much proceeds will you receive?

€

P = F(1− dt)

€

=80,000 1− (.03) 1 212( )[ ]

€

=Php77,200

1.2 Discount Interest1.2 Discount Interest

17. Find the term of a loan whose proceeds and maturity value are Php56,225 and Php65,000, respectively. The discount interest rate applied is 6%.

€

t =F − P

Fd

€

=65,000 − 56,225

(65,000)(.06)

€

=2.25 years

1.2 Discount Interest1.2 Discount Interest

21. Find the amount due at the end of 15 months if the present value is Php18,000 and if

a) the discount interest rate is 5%b) the simple interest rate is 5%

€

F =P

1− dt

€

F = P(1+ rt)

€

=18,000

1 − (.05) 1512( )

€

F = Php19,200€

=18,000 1+ (.05) 1512( )[ ]

€

=Php19,125

1.2 Discount Interest1.2 Discount Interest

27. If the discount interest rate is 11 %, how much time is needed for Php54,700 to become Php60,000?

€

58

€

t =F − P

Fd

€

=60,000 − 54,700

(60,000)(.11625)

€

=0.76 year