qs 9-12 (algo) computing note interest and maturity date lo c2\ndetermine the maturity date and compute…

qs 9-12 (algo) computing note interest and maturity date lo c2\ndetermine the maturity date and compute interest for each note.\nnote: use 360 days a year. do not round intermediate calculations.\nnote contract date principal interest rate period of note (term)\n1. march 10 $ 21,000 7% 60 days\n2. may 24 24,000 9 90 days\n3. october 21 17,000 4 45 days\ncontract date maturity month maturity date interest\n1. march 10\n2. may 24\n3. october 21

qs 9-12 (algo) computing note interest and maturity date lo c2\ndetermine the maturity date and compute interest for each note.\nnote: use 360 days a year. do not round intermediate calculations.\nnote contract date principal interest rate period of note (term)\n1. march 10 $ 21,000 7% 60 days\n2. may 24 24,000 9 90 days\n3. october 21 17,000 4 45 days\ncontract date maturity month maturity date interest\n1. march 10\n2. may 24\n3. october 21

Answer

Explanation:

Step1: Calculate days remaining in start - month

For each note, find the number of days remaining in the month of the contract date.

  1. For the note with contract date March 10: March has 31 days, so days remaining in March = 31 - 10=21 days.
  2. For the note with contract date May 24: May has 31 days, so days remaining in May = 31 - 24 = 7 days.
  3. For the note with contract date October 21: October has 31 days, so days remaining in October = 31 - 21=10 days.

Step2: Determine maturity month and date

  1. For the 60 - day note starting on March 10: After using 21 days in March, we need 60 - 21 = 39 days more. April has 30 days, so after April we still need 39 - 30 = 9 days. So the maturity month is May and the maturity date is 9th.
  2. For the 90 - day note starting on May 24: After using 7 days in May, we need 90 - 7 = 83 days more. June has 30 days, July has 31 days, so in total from June and July we have 30 + 31 = 61 days. Then we still need 83 - 61 = 22 days. So the maturity month is August and the maturity date is 22nd.
  3. For the 45 - day note starting on October 21: After using 10 days in October, we need 45 - 10 = 35 days more. November has 30 days, so we still need 35 - 30 = 5 days. So the maturity month is December and the maturity date is 5th.

Step3: Calculate interest

The simple - interest formula is $I = P\times r\times t$, where $P$ is the principal, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Since we use 360 days a year, $t=\frac{\text{number of days of the note}}{360}$.

  1. For $P = 21000$, $r=0.07$, and $t=\frac{60}{360}$: $I = 21000\times0.07\times\frac{60}{360}=\frac{21000\times0.07\times60}{360}=245$
  2. For $P = 24000$, $r = 0.09$, and $t=\frac{90}{360}$: $I=24000\times0.09\times\frac{90}{360}=\frac{24000\times0.09\times90}{360}=540$
  3. For $P = 17000$, $r = 0.04$, and $t=\frac{45}{360}$: $I=17000\times0.04\times\frac{45}{360}=\frac{17000\times0.04\times45}{360}=85$

Answer:

Contract Date Maturity Month Maturity Date Interest
March 10 May 9 245
May 24 August 22 540
October 21 December 5 85