If government revenues in 2011 were $2.2 trillion and government outlays were $3.8 trillion, the federal: choose one:
a. debt increased $1.6 trillion.
b. budget was balanced.
c. debt decreased $1.6 trillion.
d. debt was unaffected in that year.
e. budget surplus was $1.6 trillion.

The correct answer is A) Debt increased by $1.6 trillion

Explanation:

To find whether the government has a surplus or a deficit, we use this simple formula:

Govt surplus/deficit = G-T

where G = government outlays, and T= government revenue or taxes.

Now, we simply replace the terms

Because in this equation G > T, the government is in deficit, the deficit equals $1.6 billion, and will have to be financed by issuing debt. Hence, debt will increase by the same amount.

e) Bank B: 3.69%, compounded monthly

Explanation:

Since the interest is compounded for different periods in the options given, find the Effective Annual Interest rate for each Bank. This will be a fair comparison for each option.

Where,

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

Therefore,

Bank C: 3.70% compounded semi-annually

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.70%/2) ^ 2 - 1

                                                  = 7.12 %

Bank E: 3.65% compounded quarterly

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.65%/4) ^ 4 - 1

                                                  = 12.38 %

Bank D: 3.67% compounded continuously

Effective Annual Interest Rate = e ^ i - 1

                                                  = 2.7182818 ^ 3.67% - 1

                                                  = 3.74

Bank A: 3.75%, compounded annually

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.75%/1) ^ 1 - 1

                                                  = 3.75 %

Bank B: 3.69%, compounded monthly

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.69%/12) ^ 12 - 1

                                                  = 23.96 %

Conclusion

Choose the option that is giving the highest Effective Annual Interest Rate. Therefore, choose e) Bank B: 3.69%, compounded monthly.