How do I calculate the future value of the following?
$5,000 compounded annually at 12% for 2 years
$5,000 compounded semiannually at 12% for 2 years
$5,000 compounded quarterly at 12% for 2 years
$5,000 compounded monthly at 12% for 2 years
Walter's savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly?
To calculate the future value of an investment, you can use the following formula:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
Let's calculate the future value for the given scenarios:
1. $5,000 compounded annually at 12% for 2 years:
Future Value = $5,000 * (1 + (0.12 / 1))^(1 * 2)
= $5,000 * (1 + 0.12)^2
= $5,000 * (1.12)^2
= $5,000 * 1.2544
= $6,272
So, the future value of $5,000 compounded annually at 12% for 2 years is $6,272.
2. $5,000 compounded semiannually at 12% for 2 years:
Since the interest is compounded semiannually, we need to adjust the formula slightly:
Future Value = $5,000 * (1 + (0.12 / 2))^(2 * 2)
= $5,000 * (1 + 0.06)^4
= $5,000 * (1.06)^4
≈ $5,000 * 1.262476
≈ $6,312.38
So, the future value of $5,000 compounded semiannually at 12% for 2 years is approximately $6,312.38.
3. $5,000 compounded quarterly at 12% for 2 years:
Using the same adjustment as in the previous case, the formula becomes:
Future Value = $5,000 * (1 + (0.12 / 4))^(4 * 2)
= $5,000 * (1 + 0.03)^8
= $5,000 * (1.03)^8
≈ $5,000 * 1.26532
≈ $6,326.59
So, the future value of $5,000 compounded quarterly at 12% for 2 years is approximately $6,326.59.
4. $5,000 compounded monthly at 12% for 2 years:
For monthly compounding, we need to make another adjustment:
Future Value = $5,000 * (1 + (0.12 / 12))^(12 * 2)
= $5,000 * (1 + 0.01)^24
≈ $5,000 * 1.26709
≈ $6,335.45
So, the future value of $5,000 compounded monthly at 12% for 2 years is approximately $6,335.45.
Remember to adjust the formula based on the compounding period and plug in the appropriate values to calculate the future value for different scenarios.