What is the future value in 14 years of an ordinary annuity cash flow of $1,632 every quarter of a year at the end of the period, at an annual interest rate of 9.40 percent per year, compounded quarterly?
Round the answer to two decimal places.
Calculating the future value of an ordinary annuity involves determining the worth of a series of equal cash flows received or paid at regular intervals in the future, considering compounding interest. In this case, we are tasked with finding the future value of quarterly cash flows of $1,632 over a 14-year period at an annual interest rate of 9.40 percent compounded quarterly.
To solve this financial problem, we can employ the future value of an ordinary annuity formula:
��=���×(1+�/�)��−1(�/�)
Where:
FV is the future value of the annuity.
Pmt is the payment amount per period ($1,632 in this case).
r is the annual interest rate (9.40 percent or 0.094 as a decimal).
n is the number of times the interest is compounded per year (quarterly, so 4).
t is the number of years (14 in this scenario).
Now, let’s calculate the future value:
��=1,632×(1+0.094/4)4×14−1(0.094/4)
First, we simplify the equation within the parentheses:
��=1,632×(1+0.0235)56−10.0235
Now, calculate the expression within the brackets:
��=1,632×(1.0235)56−10.0235
Now, calculate the exponent:
��=1,632×2.9832−10.0235
Subtract 1 from 2.9832:
��=1,632×1.98320.0235
Finally, divide to find the future value:
��≈1,632×84.3830≈137,592.46
So, the future value of the ordinary annuity with quarterly cash flows of $1,632 each, at an annual interest rate of 9.40 percent compounded quarterly over 14 years, is approximately $137,592.46 when rounded to two decimal places.
This calculation illustrates the potential growth of an investment or savings plan with regular contributions and compound interest over time. It’s a valuable concept for individuals and businesses alike when planning for their financial future.
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