Question 1136230: Questions 2 and 3 are based on the following situation:
On 5 April Sam invested R75 000 in an account paying 8,37% interest per year, compounded monthly. Interest
is credited on the 1st of every month. Sam wants to open a second-hand cellphone shop in the new Talk-and-
Listen complex. He will move into his new premises on 21 November of the same year.
Question 2
If simple interest is used for odd period calculations and compound interest for the full term, then the amount
of money that Sam will have available in the account on 21 November is
[1] R78 195,04.
[2] R78 955,68.
[3] R79 002,95.
[4] R79 018,82.
[5] R79 020,96.
Question 3
If fractional compounding is used for the full term then Sam will receive
[1] R78 439,73.
[2] R78 896,69.
[3] R79 020,29.
[4] R79 027,82.
[5] R79 047,39.
Found 2 solutions by Tumie, ikleyn:
Answer by Tumie(1)   (Show Source):
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website! .
Questions 2 and 3 are based on the following situation:
On 5 April Sam invested R75 000 in an account paying 8,37% interest per year, compounded monthly. Interest
is credited on the 1st of every month. Sam wants to open a second-hand cellphone shop in the new Talk-and-
Listen complex. He will move into his new premises on 21 November of the same year.
Question 2
If simple interest is used for odd period calculations and compound interest for the full term, then the amount
of money that Sam will have available in the account on 21 November is
[1] R78 195,04.
[2] R78 955,68.
[3] R79 002,95.
[4] R79 018,82.
[5] R79 020,96.
Question 3
If fractional compounding is used for the full term then Sam will receive
[1] R78 439,73.
[2] R78 896,69.
[3] R79 020,29.
[4] R79 027,82.
[5] R79 047,39.
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I will solve here first part, only.
As the problem is worded, the context is that "a month" is considered as 30 days.
Then, to be consistent, the year is 12*30 = 360 days.
The general formula for the future value is
FV =  ,
where n is the number of days from April,5 to April,30;
m is the number of full months from May to October, inclusive (m = 6);
k is the number of days from Novemver,1 to November,21.
Next, the problem does not instruct on how to count the first day and the last day, but I will take the numbers
n = 30-5 = 25;
k = 21 - 1 = 20.
Then the formula becomes
FV =  .
I am copying this formula to Excel cell and obtain the answer in one click
FV = 79014.21 (rounded to the closest cent).
It is close to option (4).
There is some small discrepancy, but I do not know what is its source.
Solved in the best way I can provide.
I do not think that you really need a precise value
(since it depends on many details that are not described/instructed in the problem).
Instead, I think that you really need a right method / (methodology) to play with it quickly.
If you want to play further with it, you may separate the formula into a series
of consecutive calculations and perform each multiplication step separately,
rounding every intermediate value to the closest cent.
If so, then you can adopt/employ Excel spreadsheet for this goal.
But it is just not a mathematical game - it is the game with the software.
===================
To get basic knowledge on simple interest and compound interest problems, see the lessons
- Simple interest percentage problems
- Compounded interest percentage problems
at this site. They are free of charge.
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