We have been given that a bank offers a four year cd with an interest rate of 2.75%. The penalty for early withdrawal from the CD is nine months of simple interest, calculated on the amount withdrawn. Rachel withdraws $2250 after one year. We are asked to find the amount of penalty.
We will use simple interest formula to solve our given problem.
, where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
![2.75\%=\frac{2.75}{100}=0.0275](https://tex.z-dn.net/?f=2.75%5C%25%3D%5Cfrac%7B2.75%7D%7B100%7D%3D0.0275)
Since our given time is in months, so we need to convert 9 months into year.
1 year = 12 months
9 months = ![\frac{9}{12}\text{ year}=0.75\text{ year}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B12%7D%5Ctext%7B%20year%7D%3D0.75%5Ctext%7B%20year%7D)
Upon substituting our given values in simple interest formula, we will get:
![I=\$2250\times 0.0275\times 0.75](https://tex.z-dn.net/?f=I%3D%5C%242250%5Ctimes%200.0275%5Ctimes%200.75)
![I=\$46.40625](https://tex.z-dn.net/?f=I%3D%5C%2446.40625)
Upon rounding to nearest dollar, we will get:
![I\approx \$46](https://tex.z-dn.net/?f=I%5Capprox%20%5C%2446)
Therefore, the penalty will be $46 and option 'a' is the correct choice.