Question

What is the effective interest rate of an 8% 13-week Treasury bill? Assume it is a $10,000 Treasury bill, and round your answer to the nearest hundredth percent.

Answer 1

Answer:

The answer is 8.24%.

Step-by-step explanation:

The rate r = 8% is for 1 year or 52 weeks.

As given there are 13 weeks term so total there will be = 4 terms.

So, n = 4

The effective interest rate R is given by:

R = $(1+r/n)^n-1$

= $(1+0.08/4)^4-1$

= $(1.02)^4-1$

= 0.0824

And in percentage, it is 8.24%.

Answer 2

The effective interest rate is $\boxed{8.24\% }$ and the interest is $\boxed{200}.$

Further explanation:

The compound interest rate formula can be expressed as follows,

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

Here, A represents the amount, P represents the principal amount, i represents the interest rate and n represents the time.

The interest rate in a year is known as the effective interest rate.

The relationship between effective interest rate and nominal interest rate can be expressed as follows,

$\boxed{i = {{\left( {1 + \dfrac{{{i^n}}}{n}}\right)}^n} - 1}$

Here, i represents the effective interest rate, ${i^n}$ represents the nominal interest rate, n represents the period of interest rate.

Given:

The nominal interest rate is $8\%$ in a 13 week treasury bill.

The amount of Treasury bill is $\ 10000.$

Explanation:

There are 52 weeks in a year.

The value of n can be calculated as follows,

$\begin{aligned}n&= \frac{{52}}{{13}}\\&= 4\\\end{aligned}$

The effective interest rate can be calculated as follows,

$\begin{aligned}i&= {\left( {1 + \frac{{0.08}}{4}} \right)^4} - 1\\&= {\left( {1.02} \right)^4} - 1\\&= 0.0824\\\end{aligned}$

The interest can be calculated as follows,

$\begin{aligned}{\text{Interest}}&= P\times i \times t\\&= 10000\times 0.08 \times \frac{{13}}{{52}}\\&= 200\\\end{aligned}$

The effective interest rate is $\boxed{8.24\% }$ and the interest is $\boxed{200}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Compound interest

Keywords: Principal, invested, interest rate, account, effective interest rate, total interest, 8\% Treasury bill, nearest hundredth percent, amount.