Question

13. Mike Kornas signed a 12-month, 9% p.a. simple interest promissory note for $9,725 with MacDonald’s Furniture. After 85 days, MacDonald’s Furniture sold the note to the Royal Bank at a rate of 11%, then Royal Bank resold the note to Friendly Finance Company 42 days later at a rate of 6.25%. Find the gain or loss on this note for each company and bank involved, as well as a rate of return realized. (Don’t forget to add 3 grace days to the term of the promissory note)

Answer 1

Note bought by MacDonald's Furniture:

Present Worth of note = $9,725 | Rate of interest = 9% p.a | Term =12 month+3 days grace period = 365+3 = 368 days

Note: As per the question, added 3 days in the term, otherwise, would have used only 365 days as the term.

Using the Simple Interest formula, we can calculate Future worth of the Note.

Future Worth = Present worth * (1 + Rate of interest * Time)

Future Worth = 9,725 * (1 + 9% * 368 / 365)

Future Worth of the note = 9,725 * 1.09074

Future Worth of the note = $10,607.44

MacDonald's Furniture sold the note to Royal Bank:

Days elapsed = 85 days | Rate of interest = 11%

Remaining Term of the note = Original term - Days elapsed = 368 - 85 = 283 days

Now rearranging the Future worth formula used above, we will calculate the Present Worth of Note with new terms.

Present Worth of note after 85 days = Future Worth / (1 + New rate * Remaining days / 365)

Present Worth of note after 85 days = 10,607.44 / (1 + 11% * 283 / 365)

Present Worth of note after 85 days = 10,607.44 / 1.08529

Present Worth of note after 85 days = $ 9,773.85

MacDonald's Furniture Buy Price = $ 9,725

MacDonald's Furniture Sell Price = $ 9,773.85

Gain for MacDonald's Furniture = Sell Price - Buy Price = 9,773.85 - 9,725 = $ 48.85

Rate of Return for MacDonald's Furniture = Gain / Buy Price = 48.85 / 9,725 = 0.5024% or 0.50%

Royal Bank sold the note to Friendly Finance Company:

Days elapsed since Royal Bank bought the note = 42 days

Total Days elapsed in Note's term = Days after MacDonald's Furniture sold + Days after Royal Bank sold

Total Days elapsed in Note's term = 85 + 42 = 127 days

Remaining days in Note's Term = Original term - Total days elapsed = 368 - 127 = 241 days

Rate of Interest = 6.25%

Now we will calculate the Present worth of the note after 127 days elapsed.

Present Worth of note after 127 days = Future Worth / (1 + New rate * Remaining days / 365)

Present Worth of note after 127 days = 10,607.44 / (1 + 6.25% * 241 / 365)

Present Worth of note after 127 days = 10,607.44 / 1.04127

Present Worth of note after 127 days = $10,187.05

Royal Bank's Buy Price = $ 9,773.85

Royal Bank's Sell Price = $10,187.05

Gain for Royal Bank = Sell Price - Buy Price = 10,187.05 - 9,773.85 = 413.20

Rate of return = Gain / Buy Price = 413.20 / 9,773.85

Rate of return for Royal Bank = 4.228% or 4.23%

Since there is no transaction after note was sold to Friendly Finance Company (FFC), therefore, FFC would receive the Future worth of note.

FFC's Buy Price = $10,187.05

FFC's receipt at the end of note's term = $10,607.44

Gain for Friendly Finance Company = Note's maturity receipt - Buy Price = 10,607.44 - 10,187.05

Gain for Friendly Finance Company = $ 420.39

Rate of Return = Gain / Buy Price

Rate of Return for Friendly Finance Company = 420.39 / 10,187.05 = 4.127% or 4.13%