Answer:
- simple interest: $6500.00
- compounded annually: $6719.58
- compounded monthly: $6746.77
Explanation:
You want the value in 10 years of a savings account that earns 3% interest, in which you have deposited $5000.
Interest
The amount of money you have in 10 years will depend on the way the account earns interest. The problem statement does not mention compound interest, so one possibility is that interest is not compounded. Another possibility is that interest is compounded annually. More conventionally, a savings account will earn interest compounded monthly.
Here, we figure it three ways, so you can choose the answer that fits with the context of the problem. (If you're studying simple interest, for example, you would choose that answer.)
Simple interest
The value of an account that earns simple interest at rate r for t years is ...
A = P(1 +rt)
A = $5000(1 + 0.03·10) = $6500.00
You will have $6500 if the account earns simple interest.
Compounded annually
The value of an account that is compounded n times per year is ...
A = P(1 +r/n)^(nt)
A = $5000(1 +.03)^(1·10) = $5000(1.03^10) ≈ $6719.58
You will have $6719.58 if the account has interest compounded annually.
Compounded monthly
When interest is compounded 12 times per year (monthly), the value is ...
A = $5000(1 +.03/12)^(12·10) = $5000(1.0025^120) ≈ $6746.77
You will have $6746.77 if the account has interest compounded monthly.
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Additional comment
We don't like to make assumptions about the intent of the problem, so we'll leave that to you. We expect you will have example problems or other contextual information that will help you understand what this problem is asking.
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