MATHEMATICS HIGH SCHOOL

Craig is considering four loans. Loan L has a nominal rate of 8.254%, compounded daily. Loan M has a nominal rate of 8.474%, compounded weekly. Loan N has a nominal rate of 8.533%, compounded monthly. Loan O has a nominal rate of 8.604%, compounded yearly. Which of these loans will offer Craig the best effective interest rate?

Answers

Answer 1

Answer:

Loan L that has a nominal rate of $8.254\%$ , compounded daily offer Craig the best effective interest rate.

Further explanation:

Given:

The options are as follows,

(a). Loan L has a nominal rate of $8.254\%$ , compounded daily.

(b). Loan M has a nominal rate of $8.474\%$ , compounded weekly.

(c). Loan N has a nominal rate of $8.533\%$ , compounded monthly.

(d). Loan O has a nominal rate of $8.604\%$ , compounded yearly.

Explanation:

The compound interest rate formula can be expressed as follows,

$\boxed{A = P{{\left( {1 + (r)/(n)} \right)}^(nt)}}$

Here, A represents the amount, P represents the principal amount, r represents the interest rate n represents the number of times interest rate compounded and t represents the time.

Consider the amount as $\$100$ for 2 years.

The amount after year if the interest rate is $8.254\%$ , compounded daily can be calculated as follows,

$\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08254}}{{365}}} \right)^(2 * 365)} \n&= \$ 117.95 \n\end{aligned}$

The amount after year if the interest rate is $8.474\%$ , compounded weekly can be calculated as follows,

$\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08474}}{{52}}} \right)^(2 * 52)}\n&= \$ 118.45 \n\end{aligned}$

The amount after year if the interest rate is $8.533\%,$ compounded monthly can be calculated as follows,

$\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08533}}{{12}}} \right)^(2 * 12)}\n&= \$ 118.54\n\end{aligned}$

The amount after year if the interest rate is $8.254\%$ , compounded daily can be calculated as follows,

$\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08604}}{1}} \right)^(2 * 1)} \n&= \$ 117.95\n\end{aligned}$

Loan L that has a nominal rate of $8.254\%$ , compounded daily offer Craig the best effective interest rate.

Option (a) is correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is not correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Simple interest

Keywords: Craig, four loans, loan L, loan M, loan N, loan O, nominal rate, compounded daily, effective rate, compounded monthly, compounded weekly, compounded yearly, interest rate, Principal, invested, interest rate, account, effective interest rate, total interest, amount.

Answer 2

Answer: In order for you to be able to determine on which is the best effective interest rate, we need to compute each interest and see on how much would it accrue after it matures. The formula to use is the compound interest formula which is A=P(1+r/n)^nt, wherein A is the amount of due including the interest, P as the principal, r as the interest rate, n as the number of times it would be compounded per year and t as the number of years it would be loaned. To reassign the formula with each given interest rate, and assuming that the amount to be loaned would be 1,000 and the number of years it would be loaned will be 5 years, the amount due after 5 years for the 8.254% compounded daily will be 1,510.82, for the 8.474% compounded weekly will be 1,527.03, for the 8.533% compounded monthly will be 1,529.80, for the 8.604% compounded yearly will be 1,510.88. The best effective interest rate offer would be the 8.254% compounded daily.

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Answers

Answer:

Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Step-by-step explanation:

Given: Sequence = 10, 9.5 , 9 , 8.5 , 8

To find: Explicit Formula for the sequence and 8th term of sequence

1st term of sequence = 10

2nd term of sequence = 9.5

3rd term of sequence = 9

4th term of sequence = 8.5

5th term of sequence = 8

Difference between 2nd and 1st term = 9.5 - 10 = -0.5

Difference between 3rd and 2nd term = 9 - 9.5 = -0.5

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$a_n=10.5-0.5n$

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Answer:

The term number eight is 6.5

$a_(8)=6.5$

Step-by-step explanation:

The given sequence is an arithmetic sequence, because each term can be found by applying a difference.

In this case, you can observe that such difference is -0.5, because each term is going down by 0.5 units.

The formula that describes an arithmetic sequence is

$a_(n)=a_(1)+(n-1)d$

Where $a_(n)$ is the last term, $a_(1)$ is the first term, $n$ is the position of the last term and $d$ is the difference.

Each variable is

$a_(1) =10\nd=-0.5\nn=8\n$

Where we are gonna find $a_(8)$ the term number eight. So, replacing values, we have

$a_(n)=a_(1)+(n-1)d\na_(8)=10+(8-1)(-0.5)\na_(8)=10+7(-0.5)=10-3.5\na_(8)=6.5$

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