SOLUTION: Hi, I would very much appreciate help with this problem: Decide whether the statement makes sense, and explain your reasoning. John is planning to invest his money for one year

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Question 1135874: Hi,
I would very much appreciate help with this problem:
Decide whether the statement makes sense, and explain your reasoning. John is planning to invest his money for one year only. He chose an account paying simple interest at 6% per year which was clearly a better deal than an account paying a 5.9% APR with interest compounded annually.
Thank you!
Found 4 solutions by rothauserc, Edwin McCravy, MathTherapy, greenestamps:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
Let's say that John invested $1000
:
1) simple interest(SI) calculation, SI = (P * r * t)/100, P is principle, r is rate and t is time in years)
:
(1000 * 6 * 1)/100 = $60
:
After 1 year, John has $1060 in his account
:
2) compound interest calculation, A = P(1 +(r/n*100))^(nt), A is amount after t years, n is number of times the interest is compounded yearly, r is rate
:
Amount after 1 year = 1000(1 +(5.9/(1 * 100))^1 = 1059
:
Simple interest will give John $1 more than compound interest
:
***************
John is correct
***************
:

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Simple interest formula          Compound interest formula
  A = P∙(1+r∙t)                           A = P∙(1+r/n)nt
  A = P∙(1+0.06∙t)                        A = P∙(1+0.059/1)(1)t
                                          A = P∙(1.059)t 

After 1 year

  A = P∙(1+0.06∙1)                        A = P∙(1.059)1
  A = P∙(1.06)                            A = P∙(1.059)

Multiplying the principle by 1.06 is slightly better than multiplying by 1.059. So
the simple interest is a slightly better deal ONLY because he is planning to
invest his money for one year only.  If he were planning to invest his money for
two years or more, then the compound interest would be slightly better. 

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hi,
I would very much appreciate help with this problem:
Decide whether the statement makes sense, and explain your reasoning. John is planning to invest his money for one year only. He chose an account paying simple interest at 6% per year which was clearly a better deal than an account paying a 5.9% APR with interest compounded annually.
Thank you!
Simple interest FV amount, or 

Compound interest FV amount, or 

Which is better? You decide, and explain why you made that choice! 

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


If investing for one year only, x percent compounded annually is the same as x percent simple interest, because there is no compounding.


And 6% is better than 5.9%. 

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