Your fixed expenses are $1,151.65/month. You saved 4 months' worth in an emergency fund, investing 25% in a savings account at a 3.3% APR and the rest in a 60-day CD at a 4.3% APR. How much total interest accrues over 60 days? Round any decimals to the nearest penny.


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1 answer

First, we need to calculate the total amount saved in the emergency fund:

\[ 4 \text{ months} \times 1,151.65 \text{ dollars/month} = 4,606.60 \text{ dollars} \]

Now, let's break down how the money is allocated:

  • 25% in a savings account: \[ 0.25 \times 4,606.60 = 1,151.65 \text{ dollars} \]

  • 75% in a 60-day CD: \[ 0.75 \times 4,606.60 = 3,454.95 \text{ dollars} \]

Next, we will calculate the interest accrued from both the savings account and the CD over 60 days.

Interest from the Savings Account

The annual interest rate is 3.3%, which can be converted to a daily interest rate. Since there are 365 days in a year:

\[ \text{Daily interest rate} = \frac{3.3%}{365} = \frac{0.033}{365} \approx 0.00009041096 \text{ (in decimal)} \]

Now, we calculate the interest for 60 days:

\[ \text{Interest for 60 days} = 1,151.65 \times 0.00009041096 \times 60 \]

Calculating the interest:

\[ = 1,151.65 \times 0.00009041096 \times 60 \approx 0.06249038293 \approx 0.06 \text{ dollars} \]

Interest from the 60-day CD

The annual interest rate for the CD is 4.3%, which can also be converted to a daily interest rate:

\[ \text{Daily interest rate} = \frac{4.3%}{365} = \frac{0.043}{365} \approx 0.000117808219 \text{ (in decimal)} \]

Calculating the interest for 60 days from the CD:

\[ \text{Interest for 60 days} = 3,454.95 \times 0.000117808219 \times 60 \]

Calculating this:

\[ = 3,454.95 \times 0.000117808219 \times 60 \approx 0.0246021141 \approx 0.02 \text{ dollars} \]

Total Interest Accrued

Now we will sum the interest accrued from both the savings account and the 60-day CD:

\[ \text{Total Interest} = 0.06 + 0.02 = 0.08 \text{ dollars} \]

Thus, the total interest accrued over 60 days is:

\[ \boxed{0.08} \]