Carl puts 10,000 into a bank account that pays an annual effective interest rate of 4% for ten years. If a withdrawal is made during the first five and one-half years, a penalty of 5% of the withdrawal amount is made. Carl withdraws K at the end of each of years 4, 5, 6, 7. The balance in the account at the end of year 10 is 10,000. Calculate K.

$980

Explanation:

The amount = puts in the bank is 10000

Interest rate is 4% = 0.04

Penalty = 0.05

In solving for K,

10000x1.04¹⁰-(1.05k(1.04⁶)-1.05k(1.04)⁵-(k(1.04)⁴-k(1.04)³) = 10000

10000x1.04¹⁰ is approximately 14802

When solve out 1.05k(1.04⁶)-1.05k(1.04)⁵-(k(1.04)⁴-k(1.04)³)

We get 4.9k

14802-4.9k = 10000

14802-10000 = 4.9k

4802 = 4.9k

Divide through by 4.9

4802/4.9

= 980 dollars

Please when solving pay attention to the powers and also approximate accordingly.

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