Which is the better investment over a y year term? Calculate each one.
Investment that offers a rate of 2.25% per annum, compounded semi-anually.
Investment that offers a rate of 2.15% per annum, compounded quarterly.
Investment that offers a rate of 1.95% per annum, simple interest.
How do I calculate this?
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To compare these investments, we need to calculate the final value of each investment after the given time period. The formulas for calculating the final value for each investment are as follows:
1. Investment compounded semi-annually:
Final Value = P(1 + r/n)^(n*t)
Where P is the initial principal amount, r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
2. Investment compounded quarterly:
Final Value = P(1 + r/n)^(n*t)
Where P is the initial principal amount, r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
3. Investment with simple interest:
Final Value = P(1 + r*t)
Where P is the initial principal amount, r is the annual interest rate (expressed as a decimal), and t is the number of years.
To calculate each investment, you need to plug in the given values into the respective formula.
Let's assume we invest $1000 for a period of y years and calculate the final value for each investment option.
To calculate the returns on each investment over a specific term, you'll need to use the formulas for compound interest and simple interest. Here's how you can calculate the returns for each investment:
1. Investment with a rate of 2.25% per annum, compounded semi-annually:
The formula for compound interest is: A = P(1 + r/n)^(n*t)
Where:
A = the final amount (including principal and interest)
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, the interest rate is 2.25% per annum, compounded semi-annually. So:
r = 0.0225 (convert 2.25% to decimal form)
n = 2 (compounded semi-annually)
t = y (the specified number of years)
Plug in the values into the formula and solve for A to calculate the final amount.
2. Investment with a rate of 2.15% per annum, compounded quarterly:
Using the same formula, the only difference is the number of compounding periods per year.
r = 0.0215 (convert 2.15% to decimal form)
n = 4 (compounded quarterly)
Again, substitute the values into the formula and solve for A to calculate the final amount.
3. Investment with a rate of 1.95% per annum, simple interest:
The formula for simple interest is: A = P(1 + r*t)
Where:
A = the final amount (including principal and interest)
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
t = number of years
In this case, the interest rate is 1.95% per annum.
r = 0.0195 (convert 1.95% to decimal form)
t = y (the specified number of years)
Substitute the values into the formula and solve for A to calculate the final amount.
After calculating the final amounts for each investment option, compare the results to determine which investment would provide a better return over the given y-year term. The investment with the highest final amount would be considered the better investment in this scenario.