Question

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. What is the difference in the amount of interest earned in 30 days between the two savings instruments?

$22.96


$19.12


$26.07


$15.33

Answer 1

Option A. , $22.96

Explanation:

You saved in an emergency fund = $10,943.89

You saved it in two parts, one fourth is in a regular saving account and the remainder is in a 30-day CD.

First we calculate how much money you saved in both accounts.

`(1)/(4)` × 10,943.89 = $2,735.97 is in regular savings account

Remainder = 10,943.89 - 2,735.97 = $8,207.92 is in CD.

Now we calculate interest earned in 30 days. so we use the formula :

I = prt

Where,

P = Principal amount

r = rate of interest (in decimal)

t = time 30 days (30÷365)

In regular savings account,

Principal amount = $2,735.97

Rate of interest = 3.5% =
`(3.5)/(100)` = 0.035

Time = 30 days of 365 days

I = 2735.97 ( 0.035 × 30 ÷ 365 )

I = 2735.97 ( 0.002876 )

I = $7.87

In CD account,

Principal amount = $8,207.92

Rate of interest = 4.57% = 0.0457

Time = 30 days

I = 8207.92 ( 0.0457 × 30 ÷ 365 )

I = 8207.92 ( 0.003756 )

I = $30.83

Now we got the interest for 30 days in both accounts. So the difference between the amount of interest would be

30.83 - 7.87 = $22.96

Option A. $22.96 would be correct answer.

Answer 2

I found the same question on the internet and their answer is $9.76, which is obviously not in your choices. They deducted both given interest rates before multiplying it to the emergency fund amount and dividing it by 12 months.

4.57%−3.5%
=1.07%
(0.0107×10,943.89)÷12
=9.76

Another possible answer is $22.96 using 30 days / 365 days in a year.

Savings: 10,943.89 x (1/4) x 3.5% x (30/365) = $7.87
CD: 10,943.89 x the remainder (3/4) x 4.57% x (30/365) = $30.83

The difference between the two values: 30.83 - 7.87 = $ 22.96: so the first choice (I'm not so sure though)