To calculate the total interest earned in 45 days, let's break this down step-by-step.
-
Calculate the total amount in the emergency fund: \[ \text{Total savings} = \text{Fixed expenses} \times \text{Number of months saved} \] \[ \text{Total savings} = 1,328.90 \times 4 = 5,315.60 \]
-
Divide the total savings into two parts:
- Half in a 45-day CD: \[ \text{Amount in CD} = \frac{5,315.60}{2} = 2,657.80 \]
- The remainder in a regular savings account: \[ \text{Amount in savings account} = \frac{5,315.60}{2} = 2,657.80 \]
-
Calculate the interest earned on the 45-day CD at 4.5% APR:
- First, convert the APR into a daily interest rate: \[ \text{Daily interest rate} = \frac{4.5%}{365} \approx \frac{0.045}{365} \approx 0.00012328767 \]
- Then calculate the interest for 45 days: \[ \text{Interest from CD} = \text{Amount in CD} \times \text{Daily interest rate} \times 45 \] \[ \text{Interest from CD} = 2,657.80 \times 0.00012328767 \times 45 \approx 2,657.80 \times 0.005559952 \approx 14.75 \]
-
Calculate the interest earned on the regular savings account at 3.2% APR:
- First, convert the APR into a daily interest rate: \[ \text{Daily interest rate} = \frac{3.2%}{365} \approx \frac{0.032}{365} \approx 0.0000876712 \]
- Then calculate the interest for 45 days: \[ \text{Interest from savings account} = \text{Amount in savings account} \times \text{Daily interest rate} \times 45 \] \[ \text{Interest from savings account} = 2,657.80 \times 0.0000876712 \times 45 \approx 2,657.80 \times 0.003948204 \approx 10.48 \]
-
Total interest earned: \[ \text{Total interest} = \text{Interest from CD} + \text{Interest from savings account} \] \[ \text{Total interest} = 14.75 + 10.48 = 25.23 \]
Thus, the total interest earned in 45 days is $25.23.
1 answer