question archive 1) If Sluggo borrows $1000 on a 270-day, 9-month basis, and a 4% APR: a
1) If Sluggo borrows $1000 on a 270-day, 9-month basis, and a 4% APR: a
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1) If Sluggo borrows $1000 on a 270-day, 9-month basis, and a 4% APR:
a. Using simple interest calculations
i. What is the PER?
ii. What is the EAR?
iii. What is the APR?
b. Using the discount interest calculations:
i. What is the PER?
ii. What is the EAR?
iii. What is the APR?
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Answer a
i PER is 3%
ii
EAR is 4.02%
iii
APR is 4%
b
i.
PER is 3.09%
ii
EAR is 4.14%
iii
APR is 4.12%
Step-by-step explanation
Answer a
i
PER means Periodic effective rate
Loan amount is $1000
net proceeds of loan amount under simple interest is same as $1000
interest rate is 4% APR
days = 270
months = 9 months
Interest under simple interest formula = Loan amount*APR*months/12
=1000*4%*9/12
=30
PER = Interest amount/ net proceeds of loan amount
=30/1000
=3%
So PER is 3%
ii
Effective annual rate formula = ((1+PER)^(12/months))-1
=((1+3%)^(12/9))-1
=0.04019868307 or 4.02%
So EAR is 4.02%
iii
APR = Interest rate/net proceeds*12/months
=30/1000*12/9
=0.04 or 4%
So APR is 4%
b
PER means Periodic effective rate
i.
Loan amount is $1000
interest rate is 4% APR
days = 270
months = 9 months
Interest under discount interest formula = Loan amount*APR*months/12
=1000*4%*9/12
=30
Net proceeds of loan = loan amount-interest amount
=1000-30=970
PER = Interest amount/net proceeds of loan amount
=30/970
=0.03092783505 or 3.09%
So PER is 3.09%
ii
Effective annual rate formula = ((1+PER)^(12/months))-1
=((1+0.03092783505)^(12/9))-1
=0.04144823345 or 4.14%
So EAR is 4.14%
iii
APR = Interest rate/net proceeds*12/months
=30/970*12/9
=0.0412371134 or 4.12%
So APR is 4.12%
