Answered

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You do not start saving money until age 46. On your 46th birthday you dutifully invest​ $10,000 each year until you finish your deposits when you reach the age of 65​ (you make the last deposit on your 65th​ birthday). The annual interest rate is 8​% that you earn on your deposits. Your brother starts saving​ $10,000 a year on his 36th birthday but stops making deposits after 10 years. He then withdraws the compounded sum when he reaches age 65. How much more money will your brother have than you at age​ 65?

Sagot :

Answer:

$217,600

Explanation:

The computation of the more money is shown below:

As we know that

The Future value of the annuity is

= P × { (1+r)^n - 1} ÷ r

= $10,000 × (1+.08)^20 - 1) ÷ 0.08

= $457,619.64

For 36 years to 46 years,

FV = $10,000 × (1+.08)^10 - 1) ÷ 0.08

= $144,865.62

Now

FV = PV(1+r)^n

 = $144,865.62×  (1+.08)^20

= $675,212.47

Now the more amount would be

= $675,212.47 - $457,619.64

= $217592.83

= $217,600

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