When money is lent, is is done in two ways.
Equal Interest Method
1. The principal is expected to be repaid at the end of the loam term. Regular equal interest payments are done at a specified interest. This done in loans like some collateralised loans (eg: gold loan), company loans like bonds etc. Loans can be made with or without a discount/premium.
WITHOUT DISCOUNT/PREMIUM
for eg: suppose a loan is given for an amount of $50000, for 5 yrs with an interest of 10%
jan 1 19x1
notes receivable 50000
cash 50000
dec 31
cash 10000
interest receivable 10000
dec 31 19x5
cash 10000
interest receivable 10000
cash 50000
notes receivable 50000
WITH DISCOUNT
Consider a bond issued at a rated interest of 4%. Since the market rate prevailing is 5%, the 1% difference has to be compensated to the lender by issuing the bond at a discount in order to compensate the 1% difference. This is illustrated in the following example..
The bond of $100000 par is issued at a rated interest of 4%, with a maturity period of 8 periods and the market rate is 5%. The interest payment of $4000 has to be paid to the lender, because that is what is mentioned in the bond. But in order to compensate the 1%, the bond is issued at a discount
We find the present value of the principal by finding the present value of the principal and the payments at the actual interest rate which is the market rate ie at 5% for 8 periods..
Present value of $100000 @ 5% int for 8 years+ the present value of all the $4000 payments (8 payments)
= $93552.
This means that when we finally pay the $100000 and the 8 payments of $4000 after 8 years has only a real value for the lender of $93552. But he needs to get his $100000 at the end of the period. The interest payment of $4000 is only to maintain the value of his $10000 at the end of the period. In order to compensate for the deficit of $6448, the lender is allowed to lend only $93552 in the beginning and is assured to be paid with $100000 at the end of the term.
So at the date of receipt of cash, the entry is
cash 93552
discount 6448
bond payable 100000
At this point the amount liable to the lender is only $93552. (whatever he has paid if there is no prepayment charge)
Now when the first interest which has to be paid in cash according to the bond conditions, payed at 4% after 1 year, the entry is
interest expense 4000
cash 4000
But we have to pay 5% ie at the market rate of $93552 ( this was the actual amount liable at the beginning of the year ). This will amount to $4678. But since $4000 has already been paid, the amount to be paid is only $678. This $678 is added to the amount to be paid ie $93552 instead of paying in cash and the actual amount to be paid at the end of the period is calculated as $ 94230. The entry is
interest expense $678
discount $678
Now the amount payable at the end of the year to the lender is increased to $100000$5770=$94230. The balance of the various accounts at the end of the year is
Bond payable $100000
minus discount ( $5770 )
Net liability in the balance sheet $94230
At this point if the loan is closed, then the cash given is only $94230 ( if there is no loan pre payment charge)
Bond payable $100000
discount $5770
cash $94230
The complete table of payments is given below
Interest Period

Interest Paid
(4% of Par)

Interest Expense
(5% of Book
Value)

Amortisation

Discount Balance

Book Value

Issue date

$4000





6448

93552

1

4000

4678

678

5770

94230

2

4000

4712

712

5058

94942

3

4000

4747

747

4311

95689

4

4000

4784

784

3527

96473

5

4000

4824

824

2703

97297

6

4000

4865

865

1838

98162

7

4000

4908

908

930

99070

8

4000

4930

930

0

100000

Here the discount is also AMORTIZED over the period.
WITH PREMIUM
If bond of $100000 is issued @4% for 8 years and the market rate is only 3%, then we are over compensating the lender by 1%. In order to compensate for this extra interest payment to the lender, we issue the bonds at the premium.
By applying the same logic in a discount situation, the present value of $100000 and and $4000 interest at the actual rate of 5%= $106980. This additional $6980 is a premium we demand from the lender to compensate for the additional 1% interest we give him.
cash 106980
premium 6980
bond payable 100000
At this point the amount liable to the lender is $106980 ( if there is no prepayment charge)
Now when the first interest which has to be paid in cash according to the bond conditions, payed at 4% after 1 year, the entry is
interest expense 4000
cash 4000
But we have to pay only 3% ie at the market rate of $106980 ( this was the actual amount liable at the beginning of the year ). This will amount to $3209. But since $4000 has already been paid, the amount to be retrieved bakc is $791. This $791 is subtracted to the amount to be paid ie $106980, instead of paying in cash and the actual amount to be paid at the end of the period is calculated as $ 106189. The entry is
premium $791
interest expense $791
Now the amount payable at the end of the year to the lender is decreased to $100000+$6189=$106189. The balance of the various accounts at the end of the year is
Bond payable $100000
plus premium $6189
Net liability in the balance sheet $106189
At this point if the loan is closed, then the cash given is only $106189 ( if there is no loan pre payment charge)
Bond payable $100000
premium $6189
cash $106189
The complete table of payments is given below
Interest Period

Interest Paid
(4% of Par)

Interest Expense
(5% of Book
Value)

Amortisation

Discount Balance

Book Value

Issue date

$4000





6980

106980

1

4000

$3209

791

6189

106189

2

4000

3186

814

5375

105375

3

4000

3161

839

4536

104536

4

4000

3136

864

3672

103672

5

4000

3110

890

2782

102782

6

4000

3083

917

1865

101865

7

4000

3056

944

921

100921

8

4000

3079

921

0

100000

Here the premium is amortised over the period.
Equated Periodic Installments or Diminishing Interest Method.
WITHOUT DISCOUNT
WITHOUT DISCOUNT
2. The principal is expected to be received in installments along with the interest. This is normally done in loans like personal loans, vehicle and home loans etc
eg: a loan is made for an amount of $25000 for 3 years, the interest is 10% and the principal and the interest is expected to be paid in equated yearly installments with first installment to be paid initially.
This is an annuity due situation. To find the annuity payments, we divide the principal $25000 by the annuity due for $1.
25000/2.73554= 9139
for loan
notes receivable 25000
cash 25000
for the first payment received at the beginning of the first year,
cash 9139
notes receivable 9139
by the end of the year, an interest is accrued on the remaining notes receivable, which is recorded as an interest revenue as
notes receivable 1586
Interest revenue 1586
This process is repeated every year until the note is completely received. The interest revenue account gets accumulated with all the interest revenues of each year.
The full table of transactions in each accounts is given below
Date

Payment

Interest

Change in Receivable

Balance of
Receivable

Yr 1 Beginning







$25000

Yr 1 Beginning

$9138.96



$(9138.96)

15861.04

Yr 1 end



$1586.10

1586.1

17447.14

Yr 2 beginning

9138.96



(9138.96)

8308.18

Yr 2 end



830.82

830.82

9139.00

Yr 3 beginning

9138.96



(9138.96)

0(rounded)

Here a few points may be noted
1. In the Equal Interest Method, the interest payments are all equal in amount and the principal outstanding always stands the same.
2. In the Equated Periodic Installment method, the payment amount always is the same every period.
3. The component which goes to the principal always increases when the payments progress, while the interest component always decreases. This is evident from the table of payments in the example.
WITH DISCOUNT
A bond like discount is never given in cases of equated periodic installments. This is because, only bonds are issued at a discount or premium to the par value, in order to compensate or get compensated for the difference in interest rate from the market rate.
There are situations where the loan incurred will be with a discount in a equated periodic installment situation.
For example
Suppose a machine is bought from a dealer for an amount of $10000, and the dealer agrees to get paid in 5 equal installments, then a discount situation arises. On the face of it, this is a transaction in which the dealer does not charge interest on the delayed payments in installment and we might be surprised why he forfeits a portion of his profits in the decaying value of his payment. But he should have more than made up for it in marking up the price of the machine at the time of sale.
In order to estimate how much he might have possibly marked up in order to make up for the apparently forfeited interest, we find the present value of the payments with the imputed rate.
If the rate we use is 10%, present value of $2000 for 5 periods is $7582
Now we can see that there is a $2418 loss for the dealer in interest had he not marked up the price of the machine by the same amount. So we make belief that has has done so and believe that he compensates the loss in the interest by amortizing the discount as seen below
The entry when the machine is delivered is
machine 7582
discount 2418
notes payable 10000
At this point if the machine is returned the dealer will have to give only $7582 at the maximum
At the end of the year, for the installment payment
notes payable 2000
cash 2000
At the end of the year to compensate the dealer, we add the interest onto the amount we owe him ($7582) which is a non cash payment.
interest exp 758
discount 758
Now the amount we owe him increases to $8430. The amortization table is given below
WITH DISCOUNT
A bond like discount is never given in cases of equated periodic installments. This is because, only bonds are issued at a discount or premium to the par value, in order to compensate or get compensated for the difference in interest rate from the market rate.
There are situations where the loan incurred will be with a discount in a equated periodic installment situation.
For example
Suppose a machine is bought from a dealer for an amount of $10000, and the dealer agrees to get paid in 5 equal installments, then a discount situation arises. On the face of it, this is a transaction in which the dealer does not charge interest on the delayed payments in installment and we might be surprised why he forfeits a portion of his profits in the decaying value of his payment. But he should have more than made up for it in marking up the price of the machine at the time of sale.
In order to estimate how much he might have possibly marked up in order to make up for the apparently forfeited interest, we find the present value of the payments with the imputed rate.
If the rate we use is 10%, present value of $2000 for 5 periods is $7582
Now we can see that there is a $2418 loss for the dealer in interest had he not marked up the price of the machine by the same amount. So we make belief that has has done so and believe that he compensates the loss in the interest by amortizing the discount as seen below
The entry when the machine is delivered is
machine 7582
discount 2418
notes payable 10000
At this point if the machine is returned the dealer will have to give only $7582 at the maximum
At the end of the year, for the installment payment
notes payable 2000
cash 2000
At the end of the year to compensate the dealer, we add the interest onto the amount we owe him ($7582) which is a non cash payment.
interest exp 758
discount 758
Now the amount we owe him increases to $8430. The amortization table is given below
Date

Payment

Change in net
payable (payablediscount)

Balance of net
payable

Interest on the net
payable in one year

Change in net Payable
(payablediscount)

Balance of net
payable

Yr 1 Beginning









$(2418)

$7582

Yr 1 end

$2000

$(2000)

$5582

$758.2

$758.2

6340.2

Yr 2 end

2000

(2000)

4340.2

634.02

634.02

4974.2

Yr 3 end

2000

(2000)

2974.2

497.4

497.4

3471.6

Yr 4 end

2000

(2000)

1471.6

347.2

347.2

1818.8

Yr 5 end

2000

(2000)

(182)

182

182

0

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