Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the fo
2 answers:
Answer:
c) A and B, being r(loan a)= 9.699% annually, r(loan b)=9.862% annual
Step-by-step explanation:
Hi, well, let´s transform all this nominal rates into effective annual rates.
Loan A: 9.265% nominal rate, compounded weekly
In order to find the easiest effective rate, we need to divide this rate by 52 (which are the weeks in a year). Once we do that, we convert this effective weekly rate into an effective annual rate. Let´s walk you through all this.
Or 0.178173% effective weekly. Now we can transform it into an effective annual rate.
Or 9.669% annual, which is less than 9.955%, so this one is sellected, let´s check the next.
Loan B: 9.442% nominal rate, compounded monthly
Just like we did with Loan A, we need to divide this rate too, only this time, we will divide by 12, therefore obtaining an effective monthly rate.
Or 0.786833% effective monthly, let´s turn it into a effective annual rate.
Or 9.862% annual, so this rate would work for Melanie too. This means that option C) is the answer we are looking for but, let´s walk that extra mile and turn that Loan C rate into an annual rate.
or 2.42975% effective quarterly, now, let´s convert it into an effective annual rate.
That is 10.079% effective annual, therefore, Loan C is not an option for Melanie.
Best of Luck.
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a geometric sequence is a bunch of numbers where you can get from a number to the next number by multiplying the previous number by a certain number
might be confusing so here's an example
1,2,4,8,16
each term is multiplied by 2 to get next term, that number that each term is multiplied by is called the common ratio
formula for geometric sequence is
where is nth term
is first term
r is teh common ratio
n=which term
in our example
1,3, 9, 27, 81
each term is being multiplied by 3 so it is a geometric sequence and thus r=3
also first term is 1 so
so the formula is or in function notation
Answer:
Step-by-step explanation:
refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;
The factorial of an integer n is evaluated as;
Using this concept, the above expression can now be simplified as follows;
Therefore, the permutations of 5 items taken 3 at a time is 60.
The next expression, refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;
Therefore, the combinations of 6 items taken 4 at a time is 15.
The final step is to evaluate the product;