SOLUTION: Hi, my name is Christy. Our professor passes out sheets in our class and I was wondering if you could help me with one of the questions. It is the formula {A = P ( 1+R/N) nt Com

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, my name is Christy. Our professor passes out sheets in our class and I was wondering if you could help me with one of the questions. It is the formula {A = P ( 1+R/N) nt Com      Log On


   

Question 215113: Hi, my name is Christy. Our professor passes out sheets in our class and I was wondering if you could help me with one of the questions.
It is the formula {A = P ( 1+R/N) nt Compounding Interest.
My question is An investment earns 5.6% interest, compounded monthly. Find the balance in the account after 3 years if $6000 is invested initially.
I had A = $6000 ( 1 + 0.056/365) (1) (3) Is this right? I am lost on how to get the correct answer. I know the formula, but cannot figure out how to get the correct answer. Thanks.
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An investment earns 5.6% interest, compounded monthly. Find the balance in the account after 3 years if $6000 is invested initially.
I had A = $6000 ( 1 + 0.056/365) (1) (3) Is this right? I am lost on how to get the correct answer. I know the formula, but cannot figure out how to get the correct answer. Thanks.
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Since it's compounded monthly for 3 years, that's 36 periods.
The 5.6% is per year (it's not stated, but that's typical).
Amt = $6000*(1 + 0.056/12)^36
= $7094.85

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, since this balance is compounded monthly, the value of 'n' is n=12 (not 365) since 'n' is the number of times the balance is compounded annually.


A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


A=6000%281%2B0.056%2F12%29%5E%2812%2A3%29 Plug in P=6000 (initial investment), r=0.056 (this is the decimal form of 5.6% interest), n=12, and t=3 (3 years)


A=6000%281%2B0.00466667%29%5E%2812%2A3%29 Divide 0.056 by 12 to get 0.00466667


A=6000%281%2B0.00466667%29%5E%2836%29 Multiply the exponents 12 and 3 to get 36


A=6000%281.00466667%29%5E%2836%29 Add 1 and 0.00466667 to get 1.00466667


A=6000%281.1824746%29 Raise 1.00466667 to the 36 th power to get 1.1824746


A=7094.8476 Multiply 6000 and 1.182474 to get 7094.8476


A=7094.85 Round to the nearest cent.



So if you invest $6,000 at an interest rate of 5.6%, which is compounded 12 times a year for 3 years, the return is about $7,094.85 (which is rounded to the nearest cent)