1) What is the future value of $1,000
kstorm626
Answered question
2022-02-13
Answer & Explanation
nick1337
Expert2023-04-23Added 777 answers
To calculate the future value of an investment, we need to take into account the interest rate, the length of time, and the frequency at which the interest is compounded.
First, let's consider simple interest. Simple interest is calculated by multiplying the principal (the initial investment) by the interest rate and the length of time. In this case, the principal is $1,000, the interest rate is 6%, and the length of time is 1 year. Therefore, the future value of the investment after 1 year of simple interest is:
So, the future value of the investment after 1 year of simple interest is $1,060.
Now, let's consider monthly compounding. Monthly compounding means that the interest is added to the principal each month, and then the interest is calculated on the new principal amount for the next month. To calculate the future value of an investment with monthly compounding, we use the following formula:
where P is the principal, r is the interest rate, n is the number of times the interest is compounded per year (in this case, 12 for monthly compounding), and t is the length of time in years.
Using this formula, the future value of the investment after 1 year of monthly compounding is:
So, the future value of the investment after 1 year of monthly compounding is $1,061.68.
In summary, the future value of $1,000 in 1 year at 6% interest rate is $1,060 with simple interest and $1,061.68 with monthly compounding.
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