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From the lender's POV, interest is _____ for ____ _______.
From the borrowers POV, interest is the cost of consuming ____ instead of ______.
compensation for deferred consumption.
now instead of in the future.
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Higher interest rates encourage lenders....
to lend more
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If interest rate falls ____ equilibrium interest rate (i), then ____ would offer to ______.
below, borrowers would offer to pay more
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If interest rate rises ____ equilibrium interest rate (i), then the _____ would offer to ______.
above, lenders would offer to charge less
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1 month = ___ days
1 year = ___ days
1 year= ___ weeks
1 year = ___ months
- 1 month = 30 days
- 1 year= 365 days
- 1 year = 52 weeks
- 1 year =12 months
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5 days = ___ yrs
5 days = ___ months
2 weeks = ___ years
5/365 = 0.01137 years
5/30 = 0.1666 months
2/52 = 0.0385 years
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(uv)'=
= (u' * v) + (u * v')
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(u/v)'=
= [(u'*v)-(u*v')] / v²
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ax²+bx+c=0 → x=
x= -b±√(b²-4ac) / 2a
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Suppose we have 5% interest rate per year. Suppose $1,000 is lent. After 5 years, the total is...?
(Princ.) * i * t
- = 1,000 * 0.05 * 5
- = $250 ($50/yr for 5 years)
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Accumulated value of a loan is:
What is the alternative form? (When you don't have the present value)
AVₜ = (PV₀) * (1+it)
PV₀ = AVₜ / (1+it)
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Suppose the simple int. rate is 12%/yr. Suppose PVo= $1,000. Suppose t=20 years
- AV₂₀ = PV₀(1+it)
- = 1,000(1+(0.12*20))
- = $3,400
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If i=4% simple interest. How much should we deposit now to accumulate a total of $12,870 in 8 years?
Find PV₀
- PV₀= AVₜ / (1+it)
- = 12,870 / (1+(0.04*8))
- = $9,750
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Suppose that d= 6% per year (simple discount rate). Determine present value of $1,000 to be paid in:
a) 1 year
b) 10 years
c) 20 years
- .a) Pv₀= AVₜ(1-dt)
- = 1,000(1-(0.06*1))
- = $940
- b) PV₀= 1,000(1-(0.06*10))
- = $400
- c) PV₀= 1,000(1-(0.06*20))
- = $-200, Valid Restriction that t<1/d = 1/0.06
- 1/0.06= 16.67 years (which is the maximum time)
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Present Value equation for SIMPLE INTEREST
Accumulated Value equation for SIMPLE INTEREST
PV₀= AVₜ / (1+it)
AVₜ= PV₀(1+it)
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Present Value equation for SIMPLE DISCOUNT
Accumulated Value equation for SIMPLE DISCOUNT
PV₀= AVₜ(1-dt)
AVₜ= PV₀ / (1-dt)
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d= 4% per yr (simple discount rate). How much is needed to deposit now to have $12,870 in 8 years?
Find present value:
- PV₀= 12,870(1-(0.04*8))
- = $8,751.60
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d= 4% per year. If you deposit $8,751.60 now, what is the accumulated value after 8 years?
- AVₜ= PV₀ / (1-dt)
- = 8,751.60 / (1-(0.04*8))
- = $12,870
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d= 4% per year. Adam will receive $8,000 in 30 months. What is the present value?
- PV₀= AVₜ(1-dt)
- = 8,000(1-(0.04*(30/12)))
- = $7,200
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Kate borrows $1,000 now and will repay w/ a payment of $2,000 in 20 years.
a) What is the simple interest rate?
b) What is the simple discount rate?
- a) AVₜ= PV₀(1+it)
- 2,000 = 1,000(1+20i)
- 2 = 1+20i
- 1 = 20i
- i = 0.05, 5%
- b) PV₀= AVₜ (1-dt)
- 1,000 = 2,000 (1-20d)
- 0.5 = 1-20d
- -0.5 = -20d
- d = 0.025, 2.5%
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Allen borrows $1,000 now and will repay $1500 in 10 years. Find i and d (simple interest)
- AVₜ= PV₀(1+it)
- 1500 = 1000(1+10i)
- 1500 = 1000 + 10,000i
- 500 = 10,000i
- i = 0.05, 5%
- PV₀= AVₜ(1-dt)
- 1000 = 1500(1-10d)
- 1000 = 1500 - 15,000d
- -500 = -15,000d
- d = 0.03333, 3.3%
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Evan will receive $x in 2 years. Celeste will receive $400 in 1 year. Suppose i is 6%/yr simple interest. Suppose present values of the pymnts are equal. Find x.
We know PV are equal between the two. Therefore put PV₀ in-between both equations.
- Recall: PV₀ = AVₜ / (1+it)
- So, we have:
- x / (1+2(0.06)) = PV₀ = 400 / (1+1(0.06))
- x / 1.12 = 400 / 1.06
- x= (400 / 1.06)*1.12
- x= $422.64
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1+it = ...
1+it = 1/(1-dt)
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