1 2 discount-interest
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1.2 Discount Interest1.2 Discount Interest
Discount Interest
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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
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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)
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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
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1.2 Discount Interest1.2 Discount Interest
Derived formulas:
€
F =Iddt
€
d =IdFt
€
t =IdFd
€
F =P
1 − dt
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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
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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
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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
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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%
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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
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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
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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
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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
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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