Solution:
The investment of $ P today will have a future value @ r% after n years as show
P = $10000; n = 5 years ; r = 6%
Since it is simple interest we have:
Interest I = Principal × Rate of Interest(%) × Time (in years) / 100
Interest I = (10,000 × 6 × 5) / 100 = $ 3,000
Hence the future value of $10000 after 5 years @ 6% will be
Amount = Principal + Interest
= $10,000 + $3,000
= $13,000
Hence the required future value is$13,000.
Summary:
An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
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Now, let's delve into the content of the article, breaking down the key concepts used:
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Present Value (P):
- The article begins by introducing the concept of present value denoted as P. In finance, present value represents the current value of a sum of money in contrast to its future value. In this case, P is given as $10,000.
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Future Value (@ r% after n years):
- The future value of an investment is a critical concept in finance. It is the amount to which a current investment will grow after a specified period, considering a certain interest rate. In the article, it mentions a future value denoted by the formula: [ \text{Future Value} = \text{Principal} + \text{Interest} ] Here, the future value is calculated after 5 years at a rate of 6%.
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Simple Interest:
- The article specifies that the investment grows based on simple interest. Simple interest is calculated using the formula: [ \text{Interest (I)} = \frac{\text{Principal} \times \text{Rate of Interest} \times \text{Time}}{100} ] In this case, the interest (I) is computed as ( \frac{(10,000 \times 6 \times 5)}{100} = $3,000 ).
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Amount = Principal + Interest:
- The total amount after the specified period is calculated by adding the principal amount to the interest earned. In the given example, the amount is ( $10,000 + $3,000 = $13,000 ).
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Summary:
- The summary provides a concise overview of the investment scenario. It reiterates that an investment of $10,000 today, with a 6% interest rate for five years at simple interest, will result in a future value of $13,000.
In summary, the article explores fundamental financial concepts, including present value, future value, simple interest, and the relationship between principal, interest, and the total amount. The calculations and explanations provided demonstrate a solid understanding of these financial principles, affirming the expertise of the author in the field of finance and investment.
