A woman worked for 30 years before retiring. At the end of the first year of employment she deposited 5000 into an account for her retirement. At the end of each subsequent year of employment, she deposited 3% more than the prior year. The woman made a total of 30 deposits. She will withdraw 50,000 at the beginning of the first year of retirement and will make annual withdrawals at the beginning of each subsequent year for a total of 30 withdrawals. Each of these subsequent withdrawals will be 3% more than the prior year. The final withdrawal depletes the account. The account earns a constant annual effective interest rate. Calculate the account balance after the final deposit and before the first withdrawal.

$797,837

Explanation:

the first withdrawal is $50,000

the second is $51,500

and so on...

the formula that used to solve the interest rate earned by the annuity is:

$50,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / [(1 + i)³⁰ x (i - 3%)]} x (1 + i) = $5,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}

we start to simplify the equation by cancelling  {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}

[$50,000 x (1 + i)] / (1 + i)³⁰ = $5,000

now we cancel $5,000 on each side:

[10 x (1 + i)] / (1 + i)³⁰ = 1

now lets take away (1 + i):

10 / (1 + i)²⁹ = 1

things get a little bit more simple now:

10 = (1 + i)²⁹

²⁹√10 = ²⁹√(1 + i)²⁹

1.082636734 = 1 + i

i = 1.082636734 - 1 = 0.082636734 = 8.2636734%

now we replace i in any equation:

= $50,000 x {[(1 + 0.082636734)³⁰ - 1.03³⁰] / [(1 + 0.082636734)³⁰ x (0.082636734 - 0.03)]} x (1 + 0.082636734)

= $50,000 x  {[10.82636738 - 2.427262471] / [10.82636738 x 0.052636734]} x (1 + 0.082636734)

= $50,000 x  {8.399104909 / 0.56986462} x (1.082636734)

= $50,000 x 14.73877236 x 1.082636734

= $797,837

the correct answer is:

it required the president to inform congress within forty-eight hours of any new troop commitment.

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it establishes that the president can send armed forces into action abroad only by declaration of war by congress, statutory authorization, or in case of a national emergency created by attack upon the united states, its territories or possessions, or its armed forces.

it requires the president to notify congress within 48 hours of sending armed forces to military action.

answer; ///pegged exchange rate with the united states;