I need help ASAP. I don't understand how to solve this 3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45­ day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45­ day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?

There are several ways to work these. The most straightforward is to simply slog through the numbers.

3. Your emergency fund is 4 times your expenses so is
.. emergency fund = 4*(1500.45) = 6001.80
Half that amount is 3000.90.
The interest earned at 3.15% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0315*(45/365) = 11.65

The interest earned at 4.65% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0465*(45/365) = 17.20

Your total interest in 45 days is $11.65 +17.20 = $28.85


4. The calculation is the same, only the amounts are different.
The interest earned at 3.15% for 45 days on 1500.45 is
.. I = Prt = 1500.45*.0315*(45/365) = 5.83
The interest earned at 4.65% for 45 days on 4501.35 is
.. I = Prt = 4501.35*.0465*(45/365) = 25.81
The total interest earned in this scenario is $5.83 +25.81 = $31.64

This is $31.64 -28.85 = $2.79 more than the interest earned in question 3.


_____
You could work this using weighted average interest rates.
3. The rate earned is (3.15 +4.65)/2 = 3.90% for 45 days, or 0.480822% of the 6001.80 balance, about $28.86

4. The rate earned is (3.15 +3*4.65)/4 = 4.275% for 45 days, or 0.527055% of the balance. The difference is 0.046233% of the balance, or $2.77.

Note the pennies difference from the numbers above. The differences are due to the way the numbers round off when there are two accounts. The numbers above would better match what you would see at your bank.