SOLUTION: If 6000 dollars is invested in a bank account at an interest rate of 5 per cent per year compounded continuously. How many years will it take for your balance to reach 20000 dolla

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Question 1205986: If 6000 dollars is invested in a bank account at an interest rate of 5 per cent per year compounded continuously. How many years will it take for your balance to reach 20000 dollars
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
6000%2Ae%5E%280.05x%29=20000
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.
.
ignoring small fractional part, about 24 years

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

A+=+P%2Ae%5E%28r%2At%29

20000+=+6000%2Ae%5E%280.05%2At%29

20000%2F6000+=+e%5E%280.05%2At%29

20%2F6+=+e%5E%280.05%2At%29

10%2F3+=+e%5E%280.05%2At%29

0.05t+=+ln%2810%2F3%29

0.05t+=+1.203973 approximately

t+=+1.203973%2F0.05

t+=+24.07946 approximately

It takes about 24.079 years depending how you round the final answer.

Check:
A+=+P%2Ae%5E%28r%2At%29

A+=+6000%2Ae%5E%280.05%2A24.07946%29

A+=+20000.00391348 approximately
This rounds to 20,000 when rounding to the nearest cent.