SOLUTION: Can someone help me? A principal of $5,000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate? Than

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: Can someone help me? A principal of $5,000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate? Than      Log On


   

Question 54800: Can someone help me?
A principal of $5,000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate?
Thank you,
Ashley
Found 5 solutions by Cintchr, nisargk29, ikleyn, greenestamps, amalm06:
Answer by Cintchr(481) About Me  (Show Source):
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Simple interest is found using the formula

+I=prt+
+400+=+5000%28r%29%284%29+
+400+=+20000r
+400%2F20000+=+r+
+4%2F200+=+r+
+2%2F100+=+r+
+.2+=+r+
2% = r


Answer by nisargk29(1) About Me  (Show Source):
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the annual interest rate (which is/(or MUST be) under the question).


    Let me underline and highlight it: the question is/(or MUST be) about the annual interest rate, 
    not about the 4-years time period interest rate, otherwise the problem loses its educational value).


Then the equation is


5000%2A%281%2Bx%29%5E4 = 5400  ====>


%281%2Bx%29%5E4 = 5400%2F5000 = 1.08   (it is where the other tutor took his 8%)

============================================================>


1 + x = root%284%2C1.08%29 = 1.019  ====>


x = 1.9%.


Answer.  Annual interest rate was 1.9%.


Check.   5000%2A%281%2B0.19%29%5E4 = 5390,  and the difference is due to rounding.


Answer by greenestamps(13200) About Me  (Show Source):
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You did not state whether interest was simple or compounded. The first response ignored the fact that the interest was over 4 years; the second response assumed the interest was compound interest.

Because of the numbers, I suspect the intention might have been for the interest to be simple interest. If that is the case, the numbers work out easily, and we get "nice" answers.

For simple interest, the amount of interest is simply the beginning principal, P, multiplied by the interest rate, r, and multiplied by the number of years, t (for "time"):

I+=+Prt

Plugging in the numbers from your problem...
400+=+5000%28r%29%284%29
400+=+20000r
r+=+400%2F20000+=+4%2F200+=+2%2F100

The interest rate (assuming simple interest) is 2%

Answer by amalm06(224) About Me  (Show Source):
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Use the formula I=prt, where I is the interest earned, p is the principle, r is the interest rate, and t is the time period.

Then I=prt

400=5000*r*4

Solve for r and express as a percent: r=2% (Answer)