SOLUTION: Please help with the homework. 1. Calculate the total amount earned if R1200 is invested at 7.5% interest p.a. for 2.5 years. 2. Calculate the simple interest earned on investing

Algebra ->  Finance -> SOLUTION: Please help with the homework. 1. Calculate the total amount earned if R1200 is invested at 7.5% interest p.a. for 2.5 years. 2. Calculate the simple interest earned on investing      Log On


   

Question 1185719: Please help with the homework.
1. Calculate the total amount earned if R1200 is invested at 7.5% interest p.a. for 2.5 years.
2. Calculate the simple interest earned on investing R3000 at 6% interest p.a. for 4years.
3.calculate the simple interest owned on a loan of R5080 at 9% interest for 3years
4. Calculate the total amount owed if R9000 is borrowed at 15% interest p.a for 3 month s
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to solve these financial math problems:
**1. Total Amount Earned (Compound Interest):**
* Principal (P) = R1200
* Interest rate (r) = 7.5% = 0.075 (convert percentage to a decimal)
* Time (t) = 2.5 years
Since the problem says "interest p.a." (per annum), it implies compound interest. The formula for compound interest is:
A = P(1 + rt)
Where:
* A = Total amount
* P = Principal
* r = Interest rate
* t = Time
A = 1200 * (1 + 0.075 * 2.5)
A = 1200 * (1 + 0.1875)
A = 1200 * 1.1875
A = R1425
**2. Simple Interest Earned:**
* Principal (P) = R3000
* Interest rate (r) = 6% = 0.06
* Time (t) = 4 years
The formula for simple interest is:
I = Prt
Where:
* I = Simple interest
* P = Principal
* r = Interest rate
* t = Time
I = 3000 * 0.06 * 4
I = R720
**3. Simple Interest Owed:**
* Principal (P) = R5080
* Interest rate (r) = 9% = 0.09
* Time (t) = 3 years
Using the same simple interest formula:
I = 5080 * 0.09 * 3
I = R1371.60
**4. Total Amount Owed:**
* Principal (P) = R9000
* Interest rate (r) = 15% = 0.15
* Time (t) = 3 months = 3/12 = 0.25 years (convert months to years)
Using the compound interest formula (because it says "interest p.a.")
A = P(1 + rt)
A = 9000 * (1 + 0.15 * 0.25)
A = 9000 * (1 + 0.0375)
A = 9000 * 1.0375
A = R9337.50

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

To the reader of this post.

I'd like to point some deficiencies in the solution/ (in the post) by @CPhill. 

(1)  In this problem, all questions relate to  highlight%28highlight%28simple%29%29  interest - not to compound interest.

     In his post, @CPhill writes 

           "Since the problem says "interest p.a." (per annum), it implies compound interest". 

     This statement is incorrect. This phrase does not imply that the interest is compounded.



     Right after this phrase, @CPhill writes "the formula for compound interest is:  A = P*(1+rt)".

     But this formula is NOT for compound interest - it is standard formula for simple interest, ONLY.


     So, in this part, @CPhill mistakenly refers to compound interest, but factually uses 
     the formula and makes calculations for simple interest.

 

(2)  The same my notice goes for part (4), where @CPhill makes the same mistake: 

         he declares that will use the formula for compound interest, but factually uses the formula
         for simple interest.

-------------------------

A certificate from Artificial Intelligence 

        "Interest per annum" means the interest rate calculated over a period of one year, 
        essentially signifying the percentage of interest you would earn or owe on a loan 
        or investment within a single year; "per annum" is a Latin phrase meaning "by the year."


The link to this AI source

https://www.google.com/search?q=interest+per+annum+meaning&rlz=1C1CHBF_enUS1071US1071&oq=interest+per+annum+meaning&gs_lcrp=EgZjaHJvbWUyCQgAEEUYORiABDIHCAEQABiABDIICAIQABgWGB4yCAgDEAAYFhgeMggIBBAAGBYYHjIICAUQABgWGB4yCAgGEAAYFhgeMggIBxAAGBYYHjIICAgQABgWGB4yCAgJEAAYFhge0gEKMTIxOThqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8