What is the future value on 12/31/2014 of a deposit of $10,000 made of 12/31/2010 assuming interest of 16% compound quarterly.
To calculate the future value of a deposit with compound interest, we can use the formula for compound interest:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
In this case, the principal (initial deposit) is $10,000, the interest rate is 16%, and the interest is compounded quarterly. We want to find the future value on 12/31/2014, which is 4 years after the initial deposit was made on 12/31/2010.
Step 1: Convert the annual interest rate to a quarterly interest rate.
Since the interest is compounded quarterly, we need to adjust the annual interest rate accordingly. Divide the annual interest rate by the number of compounding periods per year (in this case, 4).
Quarterly Interest Rate = Annual Interest Rate / Number of Compounding Periods per Year
Quarterly Interest Rate = 16% / 4
Quarterly Interest Rate = 4%
Step 2: Calculate the number of compounding periods.
To find the number of compounding periods, multiply the number of years by the number of compounding periods per year.
Number of Compounding Periods = Number of Years * Number of Compounding Periods per Year
Number of Compounding Periods = 4 * 4
Number of Compounding Periods = 16
Step 3: Calculate the future value.
Using the formula for compound interest, plug in the values we have:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
Future Value = $10,000 * (1 + (4% / 16))^16
Future Value ≈ $10,000 * (1.01)^16
Future Value ≈ $10,000 * 1.17216
Future Value ≈ $11,721.60
Therefore, the future value of a deposit of $10,000 made on 12/31/2010, with an interest rate of 16% compounded quarterly, on 12/31/2014 is approximately $11,721.60.