Example 7: Transactions with Static Rate of interest and daily compounding
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Example 7: Transactions with Static Rate of interest and daily compounding |
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Example 7 Scenario
This example is based on the facts in Example 6. See entire scenario below for full version.
In the previous example:
| • | The credit supply agreement said there wasn't any compound interest. |
In this example:
| • | Interest is to be compounded daily. |
Demonstrated Features
| ► | Where to find the settings. |
| ► | Introduction to different compounding options. |
| ► | Daily compounding with rounding. |
| ► | Daily compounding without rounding. |
| ► | Examine relevant parts of the calculation result. |
Points of Interest
| ◆ | Compound interest is converted into principal. |
| ◆ | The balance of interest at the end will always be $0. |
| ◆ | You have a number of options with respect to rounding etc. |
Multimedia Presentation
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Entire Scenario
There are a series of transactions on Mr Smith's account - the first one is on 16 July 2004 and the last one is on 23 November 2006, the balance is currently $6704.35.
| DATE | DESCRIPTION | AMOUNT | BALANCE |
| 16/07/2004 | Invoice No. 504 | $950.05 | $950.05 |
| 24/01/2005 | Invoice No. 505 | $1,482.18 | $2,432.23 |
| 12/10/2005 | Cheque No. 439758 | $2,772.83CR | $340.60CR |
| 05/11/2005 | Invoice No. 506 | $1,313.14 | $972.54 |
| 11/11/2005 | Dishonoured Cheque Fee | $50.00 | $1,022.54 |
| 14/01/2006 | Invoice No. 507 | $3,071.38 | $4,093.92 |
| 10/04/2006 | Cheque No. 439759 | $2,950.00CR | $1,143.92 |
| 26/05/2006 | Invoice No. 508 | $7,076.15 | $8,220.07 |
| 15/07/2006 | Cheque No. 439760 | $1,447.98CR | $6,772.09 |
| 23/11/2006 | Cheque No. 439761 | $67.74CR | $6,704.35 |
He's given a lot of business over the years and has always paid up eventually, but the account has lost too much control now.
The credit supply agreement says that interest may be charged daily at a static interest rate of 7.5% per annum.
It also says that if the customer's account goes into credit (i.e. the store owes the customer) then no interest is payable to the customer.
Interest is compounded daily.
Payments are allocated to the best benefit of the store (i.e. the creditor).
We wish to calculate interest as at 21 September 2007.
Calculation Results
The results generated by the program are shown below.
Calculation Result
Example 7
SUMMARY
| • | Calculated interest on transactions, starting with principal of nine hundred and fifty dollars and five cents ($950.05), for the period 16/07/2004 to 21/09/2007 inclusive, a period of 1139 days. |
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| • | Total interest is one thousand and thirty dollars and ninety-five cents ($1,030.95). |
| • | As at 21/09/2007 the total amount owing is seven thousand seven hundred and thirty-five dollars and thirty cents ($7,735.30) comprised entirely of principal of seven thousand seven hundred and thirty-five dollars and thirty cents ($7,735.30). |
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| • | Interest compounds (i.e. calculated and converted to principal) daily. The amount will change as principal changes. Principal continues to accumulate by the amount of each day's compound interest. |
TRANSACTION HISTORY BEFORE INTEREST IS TAKEN INTO ACCOUNT
| DATE | DESCRIPTION | AMOUNT | BALANCE |
| 16/07/2004 | Invoice No. 504 | $950.05 | $950.05 |
| 24/01/2005 | Invoice No. 505 | $1,482.18 | $2,432.23 |
| 12/10/2005 | Cheque No. 439758 | $2,772.83CR | $340.60CR |
| 05/11/2005 | Invoice No. 506 | $1,313.14 | $972.54 |
| 11/11/2005 | Dishonoured Cheque Fee | $50.00 | $1,022.54 |
| 14/01/2006 | Invoice No. 507 | $3,071.38 | $4,093.92 |
| 10/04/2006 | Cheque No. 439759 | $2,950.00CR | $1,143.92 |
| 26/05/2006 | Invoice No. 508 | $7,076.15 | $8,220.07 |
| 15/07/2006 | Cheque No. 439760 | $1,447.98CR | $6,772.09 |
| 23/11/2006 | Cheque No. 439761 | $67.74CR | $6,704.35 |
PARTICULARS OF INTEREST
(a) On 16/07/2004 the opening principal was $950.05, the interest rate on debit balances was 7.5% per annum, the interest rate on credit balances was nil (0.0%), and the days per year base used to convert the annual interest rates into daily interest rates was 366.
(b) Debits and Credits are each applied to non-principal then to interest then to principal.
(c) Calculated interest on 31/12/2004 because it was the last day before the days per year base changed (from 366 to 365) on 01/01/2005. Daily compounding of interest from 16/07/2004 to 31/12/2004 inclusive at 7.5% per annum (interest rate) ÷ 366 (days per year) percent per day for 169 days amounted to $33.71.
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(d) $33.71 (interest) equals $950.05 (principal as at 16/07/2004) x (((1.0+((7.5%/100)/366))^169)-1.0) except that it is adjusted each day by rounding to whole cents.
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(e) It changed principal to $983.76 ($950.05 plus $33.71) because all interest was compounded (converted to principal).
(f) On 01/01/2005 the days per year base used to convert the annual interest rate into the daily interest rate changed to 365. The daily interest rate is now 0.02054795% on debit balances.
(g) Calculated interest on 23/01/2005 because it was the last day before the balance of principal changed on 24/01/2005. Daily compounding of interest from 01/01/2005 to 23/01/2005 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 23 days amounted to $4.60.
(h) $4.60 (interest) equals $983.76 (principal as at 01/01/2005) x (((1.0+((7.5%/100)/365))^23)-1.0) except that it is adjusted each day by rounding to whole cents.
(i) It changed principal to $988.36 ($983.76 plus $4.60) because all interest was compounded (converted to principal).
(j) Debit on 24/01/2005: "Invoice No. 505" $1,482.18. The entire amount was added to principal, leaving a new principal balance of $2,470.54 ($988.36 plus $1,482.18).
(k) Calculated interest on 11/10/2005 because it was the last day before the balance of principal changed on 12/10/2005. Daily compounding of interest from 24/01/2005 to 11/10/2005 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 261 days amounted to $136.03.
(l) $136.03 (interest) equals $2,470.54 (principal as at 24/01/2005) x (((1.0+((7.5%/100)/365))^261)-1.0) except that it is adjusted each day by rounding to whole cents.
(m) It changed principal to $2,606.57 ($2,470.54 plus $136.03) because all interest was compounded (converted to principal).
(n) Credit on 12/10/2005: "Cheque No. 439758" $2,772.83CR. The payment was applied entirely to principal, leaving a new principal balance of $166.26CR ($2,606.57 minus $2,772.83).
(o) Debit on 05/11/2005: "Invoice No. 506" $1,313.14. The entire amount was added to principal, leaving a new principal balance of $1,146.88 ($166.26CR plus $1,313.14).
(p) Calculated interest on 10/11/2005 because it was the last day before the balance of principal changed on 11/11/2005. Daily compounding of interest from 05/11/2005 to 10/11/2005 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 6 days amounted to $1.44.
(q) $1.44 (interest) equals $1,146.88 (principal as at 05/11/2005) x (((1.0+((7.5%/100)/365))^6)-1.0) except that it is adjusted each day by rounding to whole cents.
(r) It changed principal to $1,148.32 ($1,146.88 plus $1.44) because all interest was compounded (converted to principal).
(s) Debit on 11/11/2005: "Dishonoured Cheque Fee" $50.00. The entire amount was added to principal, leaving a new principal balance of $1,198.32 ($1,148.32 plus $50.00).
(t) Calculated interest on 13/01/2006 because it was the last day before the balance of principal changed on 14/01/2006. Daily compounding of interest from 11/11/2005 to 13/01/2006 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 64 days amounted to $16.00.
(u) $16.00 (interest) equals $1,198.32 (principal as at 11/11/2005) x (((1.0+((7.5%/100)/365))^64)-1.0) except that it is adjusted each day by rounding to whole cents.
(v) It changed principal to $1,214.32 ($1,198.32 plus $16.00) because all interest was compounded (converted to principal).
(w) Debit on 14/01/2006: "Invoice No. 507" $3,071.38. The entire amount was added to principal, leaving a new principal balance of $4,285.70 ($1,214.32 plus $3,071.38).
(x) Calculated interest on 09/04/2006 because it was the last day before the balance of principal changed on 10/04/2006. Daily compounding of interest from 14/01/2006 to 09/04/2006 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 86 days amounted to $76.36.
(y) $76.36 (interest) equals $4,285.70 (principal as at 14/01/2006) x (((1.0+((7.5%/100)/365))^86)-1.0) except that it is adjusted each day by rounding to whole cents.
(z) It changed principal to $4,362.06 ($4,285.70 plus $76.36) because all interest was compounded (converted to principal).
(aa) Credit on 10/04/2006: "Cheque No. 439759" $2,950.00CR. The payment was applied entirely to principal, leaving a new principal balance of $1,412.06 ($4,362.06 minus $2,950.00).
(ab) Calculated interest on 25/05/2006 because it was the last day before the balance of principal changed on 26/05/2006. Daily compounding of interest from 10/04/2006 to 25/05/2006 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 46 days amounted to $13.34.
(ac) $13.34 (interest) equals $1,412.06 (principal as at 10/04/2006) x (((1.0+((7.5%/100)/365))^46)-1.0) except that it is adjusted each day by rounding to whole cents.
(ad) It changed principal to $1,425.40 ($1,412.06 plus $13.34) because all interest was compounded (converted to principal).
(ae) Debit on 26/05/2006: "Invoice No. 508" $7,076.15. The entire amount was added to principal, leaving a new principal balance of $8,501.55 ($1,425.40 plus $7,076.15).
(af) Calculated interest on 14/07/2006 because it was the last day before the balance of principal changed on 15/07/2006. Daily compounding of interest from 26/05/2006 to 14/07/2006 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 50 days amounted to $87.77.
(ag) $87.77 (interest) equals $8,501.55 (principal as at 26/05/2006) x (((1.0+((7.5%/100)/365))^50)-1.0) except that it is adjusted each day by rounding to whole cents.
(ah) It changed principal to $8,589.32 ($8,501.55 plus $87.77) because all interest was compounded (converted to principal).
(ai) Credit on 15/07/2006: "Cheque No. 439760" $1,447.98CR. The payment was applied entirely to principal, leaving a new principal balance of $7,141.34 ($8,589.32 minus $1,447.98).
(aj) Calculated interest on 22/11/2006 because it was the last day before the balance of principal changed on 23/11/2006. Daily compounding of interest from 15/07/2006 to 22/11/2006 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 131 days amounted to $194.81.
(ak) $194.81 (interest) equals $7,141.34 (principal as at 15/07/2006) x (((1.0+((7.5%/100)/365))^131)-1.0) except that it is adjusted each day by rounding to whole cents.
(al) It changed principal to $7,336.15 ($7,141.34 plus $194.81) because all interest was compounded (converted to principal).
(am) Credit on 23/11/2006: "Cheque No. 439761" $67.74CR. The payment was applied entirely to principal, leaving a new principal balance of $7,268.41 ($7,336.15 minus $67.74).
(an) Daily compounding of interest from 23/11/2006 to 21/09/2007 inclusive at 7.5% per annum (interest rate) ÷ 365 (days per year) percent per day for 303 days amounted to $466.89.
(ao) $466.89 (interest) equals $7,268.41 (principal as at 23/11/2006) x (((1.0+((7.5%/100)/365))^303)-1.0) except that it is adjusted each day by rounding to whole cents.
(ap) It changed principal to $7,735.30 ($7,268.41 plus $466.89) because all interest was compounded (converted to principal).
(aq) Total compound interest for the period 16/07/2004 to 21/09/2007 (1139 days) is one thousand and thirty dollars and ninety-five cents ($1,030.95).
(ar) As at 21/09/2007 the total amount owing is seven thousand seven hundred and thirty-five dollars and thirty cents ($7,735.30) comprised entirely of principal because all interest was compounded (converted to principal). $7,735.30 (amount owing) equals $950.05 (starting principal) plus $1,030.95 (compound interest).
(as) Interest continues to accumulate and compound on and from 22/09/2007, starting at one dollar and fifty-nine cents ($1.59) per day on $7,735.30. It will then increase as principal increases by the amount of each day's compound interest.
(at) principal continues to accumulate on and from 22/09/2007 by the amount of each day's compound interest.
Calculation Result
Example 7
TRANSACTION HISTORY BEFORE INTEREST IS TAKEN INTO ACCOUNT
| DATE | DESCRIPTION | AMOUNT | BALANCE |
| 16/07/2004 | Invoice No. 504 | $950.05 | $950.05 |
| 24/01/2005 | Invoice No. 505 | $1,482.18 | $2,432.23 |
| 12/10/2005 | Cheque No. 439758 | $2,772.83CR | $340.60CR |
| 05/11/2005 | Invoice No. 506 | $1,313.14 | $972.54 |
| 11/11/2005 | Dishonoured Cheque Fee | $50.00 | $1,022.54 |
| 14/01/2006 | Invoice No. 507 | $3,071.38 | $4,093.92 |
| 10/04/2006 | Cheque No. 439759 | $2,950.00CR | $1,143.92 |
| 26/05/2006 | Invoice No. 508 | $7,076.15 | $8,220.07 |
| 15/07/2006 | Cheque No. 439760 | $1,447.98CR | $6,772.09 |
| 23/11/2006 | Cheque No. 439761 | $67.74CR | $6,704.35 |
INTEREST CALCULATION TABLE
| DATE | DESCRIPTION | DAYS | AMOUNT | BALANCE | PRINCIPAL | INTEREST |
| 16/07/2004 | Interest rate started at 7.5% on debit balances (0.0204918% per day). | $950.05DR | $950.05DR | $0.00DR | ||
| 31/12/2004 | Compound Interest (16/07/2004 to 31/12/2004 inclusive) | 169 | $33.71DR | $983.76DR | $983.76DR | $0.00DR |
| 01/01/2005 | Days per year changed to 365. Daily interest rate now 0.02054795% on debit balances. | $983.76DR | $983.76DR | $0.00DR | ||
| 23/01/2005 | Compound Interest (01/01/2005 to 23/01/2005 inclusive) | 23 | $4.60DR | $988.36DR | $988.36DR | $0.00DR |
| 24/01/2005 | Invoice No. 505. Entire amount added to principal. | $1,482.18DR | $2,470.54DR | $2,470.54DR | $0.00DR | |
| 11/10/2005 | Compound Interest (24/01/2005 to 11/10/2005 inclusive) | 261 | $136.03DR | $2,606.57DR | $2,606.57DR | $0.00DR |
| 12/10/2005 | Cheque No. 439758. Payment applied entirely to principal. | $2,772.83CR | $166.26CR | $166.26CR | $0.00DR | |
| 05/11/2005 | Invoice No. 506. Entire amount added to principal. | $1,313.14DR | $1,146.88DR | $1,146.88DR | $0.00DR | |
| 10/11/2005 | Compound Interest (05/11/2005 to 10/11/2005 inclusive) | 6 | $1.44DR | $1,148.32DR | $1,148.32DR | $0.00DR |
| 11/11/2005 | Dishonoured Cheque Fee. Entire amount added to principal. | $50.00DR | $1,198.32DR | $1,198.32DR | $0.00DR | |
| 13/01/2006 | Compound Interest (11/11/2005 to 13/01/2006 inclusive) | 64 | $16.00DR | $1,214.32DR | $1,214.32DR | $0.00DR |
| 14/01/2006 | Invoice No. 507. Entire amount added to principal. | $3,071.38DR | $4,285.70DR | $4,285.70DR | $0.00DR | |
| 09/04/2006 | Compound Interest (14/01/2006 to 09/04/2006 inclusive) | 86 | $76.36DR | $4,362.06DR | $4,362.06DR | $0.00DR |
| 10/04/2006 | Cheque No. 439759. Payment applied entirely to principal. | $2,950.00CR | $1,412.06DR | $1,412.06DR | $0.00DR | |
| 25/05/2006 | Compound Interest (10/04/2006 to 25/05/2006 inclusive) | 46 | $13.34DR | $1,425.40DR | $1,425.40DR | $0.00DR |
| 26/05/2006 | Invoice No. 508. Entire amount added to principal. | $7,076.15DR | $8,501.55DR | $8,501.55DR | $0.00DR | |
| 14/07/2006 | Compound Interest (26/05/2006 to 14/07/2006 inclusive) | 50 | $87.77DR | $8,589.32DR | $8,589.32DR | $0.00DR |
| 15/07/2006 | Cheque No. 439760. Payment applied entirely to principal. | $1,447.98CR | $7,141.34DR | $7,141.34DR | $0.00DR | |
| 22/11/2006 | Compound Interest (15/07/2006 to 22/11/2006 inclusive) | 131 | $194.81DR | $7,336.15DR | $7,336.15DR | $0.00DR |
| 23/11/2006 | Cheque No. 439761. Payment applied entirely to principal. | $67.74CR | $7,268.41DR | $7,268.41DR | $0.00DR | |
| 21/09/2007 | Compound Interest (23/11/2006 to 21/09/2007 inclusive) | 303 | $466.89DR | $7,735.30DR | $7,735.30DR | $0.00DR |
| Final Balance | 1139 | $7,735.30DR | $7,735.30DR | $0.00DR |
