Question

I need help ASAP. I don't understand how to solve this

Answer 1

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.