How to calculate this?
4 year term investment. The investment offers a rate of 2.25% per annum, compounded semi-annually.
Another investment offers a rate of 2.25% annum, per compounded quarterly.
Final investment offers a rate of 1.95% per annym, simple interest.
Let P be the principal invested. The amount at the end of four years will be for each scenario
1: P*(1+0.0225/2)^(4*2)
2: P*(1+0.0225/4)^(4*4)
3: P*(1.0195^4)
To calculate the future value of an investment, you can use the compound interest formula or the simple interest formula, depending on the type of investment.
1. For the first investment with a rate of 2.25% per annum, compounded semi-annually:
To calculate the future value, you can use the compound interest formula:
Future Value = Principal Amount × (1 + (Interest Rate / n))^n*t
where:
Principal Amount = Initial investment amount
Interest Rate = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, since the investment compounds semi-annually, the number of compounding periods per year (n) would be 2.
For example, let's assume the principal amount is $10,000 and the investment has a 4-year term:
Future Value = $10,000 × (1 + (0.0225 / 2))^(2*4)
= $10,000 × (1.01125)^8
= $10,000 × 1.0943
≈ $10,943
Therefore, the future value of the first investment would be approximately $10,943.
2. For the second investment with a rate of 2.25% per annum, compounded quarterly:
Similarly, we'll use the compound interest formula:
Future Value = Principal Amount × (1 + (Interest Rate / n))^n*t
In this case, the investment compounds quarterly, so the number of compounding periods per year (n) would be 4.
Using the same example as before:
Future Value = $10,000 × (1 + (0.0225 / 4))^(4*4)
= $10,000 × (1.005625)^16
= $10,000 × 1.094282
≈ $10,943
Thus, the future value of the second investment would also be approximately $10,943.
3. For the third investment with a rate of 1.95% per annum, simple interest:
The formula for calculating the future value with simple interest is simpler:
Future Value = Principal Amount × (1 + (Interest Rate * t))
Using the same example:
Future Value = $10,000 × (1 + (0.0195 * 4))
= $10,000 × (1 + 0.078)
≈ $10,780
Therefore, the future value of the third investment would be approximately $10,780.
Remember, these calculations are approximations and may vary slightly depending on rounding and compounding methods used.