24.) For the case shown in the following table, the future value of the single cash flow deposited today at the end of the deposit period if the interest is compounded annually at the rate specified equals
Single Cash Flow $27,000
Deposit Period (years) 20
Interest Rate 11%
a. $217,682.41
b. $1,733,476.40
c. $3,348.92
d. $215,009.86
To find the future value of a single cash flow deposited today at the end of the deposit period with compound interest, we can use the formula for future value:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (single cash flow deposited today)
r = Interest Rate per period
n = Number of periods (deposit period)
In this case, the Present Value (PV) is $27,000, the deposit period (n) is 20 years, and the interest rate (r) is 11%.
Now let's calculate the future value using the given information:
FV = $27,000 * (1 + 0.11)^20
To simplify the calculation, you can use a financial calculator or spreadsheet software. But if you want to calculate it manually, here's the step-by-step process:
1. Calculate (1 + r)^n:
(1 + 0.11)^20 = 4.177248878
2. Multiply the result by the Present Value (PV):
FV = $27,000 * 4.177248878
FV ≈ $112,781.67
Now, let's compare this calculated answer with the options provided:
a. $217,682.41
b. $1,733,476.40
c. $3,348.92
d. $215,009.86
Based on the calculation, none of the provided options match the calculated answer of approximately $112,781.67.
Therefore, the correct answer is not among the options provided.