Answer:
The difference in the amount of interest in 30 days between the two savings instruments is $ 23.28
Step-by-step explanation:
Given : you saved $10,943.89 in an emergency fund.
One fourth is in a regular savings account at a 3.5% APR and the remainder is in a 30-day CD at a 4.57% APR
We have to calculate the difference in the amount of interest in 30 days between the two savings instruments.
We know,
[tex]\text{Simple interest}=\frac{principal\times rate\times time}{100}[/tex]
Consider
instrument 1) One fourth is in a regular savings account at a 3.5% APR
One fourth of saving = One fourth of $10,943.89 = [tex]\frac{1}{4}\cdot10943.89=2735.97[/tex]
Thus, Interest can be calculate using above formula ,
P = 2735.97 , r = 3.5% = [tex]\frac{3.5}{12}\%[/tex] , t = 1 month
[tex]\text{Simple interest}=\frac{2735.97 \times 3.5\times 1}{12\times 100}[/tex]
Simplify , we get,
Interest is $ 7.98
instrument 2) Remaining three fourth is in a regular savings account at a 4.57% APR
One fourth of saving = One fourth of $10,943.89 = [tex]\frac{3}{4}\cdot10943.89=8207.92[/tex]
Thus, Interest can be calculate using above formula ,
P = 8207.92 , r = 4.57% = [tex]\frac{4.57}{12}\%[/tex] , t = 1 month
[tex]\text{Simple interest}=\frac{ 8207.92 \times 4.57 \times 1}{12\times 100}[/tex]
Simplify , we get,
Interest is $ 31.26
Thus, the difference in the amount of interest in 30 days between the two savings instruments = $ 31.26 - $ 7.98 = $ 23.28
