Clark Galvan
When a sum of money, P dollars, is invested at an interest rate of i% per year, the value of the investment will increase over time. The formula for calculating the simple interest earned on an investment of P dollars at an interest rate of i% is given by I = Prt, where P is the principal amount, r is the interest rate, and t is the time in years. This formula assumes that the interest is compounded annually. The balance, A, after a certain number of years can also be calculated using the formula A = P(1 + r/100)^n, where n is the number of years.
| Characteristics | Values |
|---|---|
| Interest rate | i% per year |
| Investment amount | P dollars |
| Time period | 3n years |
| Formula for balance after 2 years | A=P(1+r)^2 |
What You'll Learn
The value of the investment after a certain number of years
When a sum of money, P dollars, is invested at an interest rate of i% per year, compounded annually, the value of the investment after a certain number of years will depend on the number of years the money is invested for.
The formula for calculating the value of an investment with simple interest is I = Prt, where P is the money invested, r is the simple interest rate, and t is the time, in years, the money is invested. For example, if $2,000 is invested for 2 years at a rate of 4.2%, the simple interest earned will be $280.
If the interest is compounded annually, the formula for calculating the value of the investment after a certain number of years is A=P(1+r)^n, where P is the principal amount, r is the interest rate, and n is the number of years. For example, if $1,000 is invested at an annual interest rate of 5% compounded once a year, the balance after 2 years will be given by A=P(1+r)^2 = $1,000(1+0.05)^2 = $1,102.50.
The value of the investment will also depend on the type of interest being used. Simple interest is calculated as a percentage of the principal amount, while compound interest is calculated on the principal amount and also on the accumulated interest of previous periods.
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The simple interest on an investment
If a sum of money, P dollars, is invested at an interest rate of i% per year, compounded annually, the value of the investment will increase over time. The formula for calculating the simple interest on an investment is I = Prt, where P is the principal amount (the initial investment), r is the annual interest rate, and t is the time in years that the money is invested for. For example, if you invest $2,000 at an interest rate of 4.2% for 2 years, the simple interest earned would be $280.
When money is invested at an annual interest rate, compound interest can be calculated using the formula A=P(1+r)^n, where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years the money is invested for. This formula assumes that the interest is compounded once a year.
The value of an investment can also be calculated for different periods of time. For example, if a sum of money is invested at an interest rate of i% per year, compounded annually, the value of the investment after 3n years will be greater than the value of the investment after 2n years. The exact value will depend on the interest rate and the number of years the money is invested for.
It is important to note that the simple interest formula assumes that the interest is calculated on the principal amount only, and does not take into account any compound interest that may be earned. Compound interest, on the other hand, assumes that interest is earned on both the principal amount and any previously earned interest, resulting in exponential growth over time.
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The balance after a certain number of years
If a sum of money, P dollars, is invested at an interest rate of i% per year, compounded annually, the balance after a certain number of years will depend on the number of years the money is invested for.
For example, if P dollars are invested at an annual interest rate of r, compounded once a year, the balance, A, after 2 years is given by A=P(1+r)^2.
The simple interest I on an investment of P dollars at an interest rate r for t years is given by I=Prt.
Therefore, the balance after a certain number of years will depend on the initial investment amount, the interest rate, and the number of years the money is invested for.
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The interest rate as a percentage
When a sum of money, P dollars, is invested at an interest rate of i% per year, compounded annually, the value of the investment will increase over time. The interest rate is a percentage of the principal amount (the original sum of money invested) and is calculated as i/100. For example, if the interest rate is 5%, then i/100 = 0.05, and this value is used in the formula for calculating the future value of the investment.
The formula for calculating the future value of an investment with compound interest is A = P(1 + i/100)^n, where A is the future value, P is the principal amount, i is the interest rate (as a decimal), and n is the number of years the money is invested for. This formula assumes that the interest is compounded annually, meaning that the interest earned each year is added to the principal amount, and the new total is used to calculate the interest for the next year.
For example, let's say you invest $1000 at an interest rate of 5% compounded annually. After one year, the future value of your investment would be A = $1000(1 + 0.05)^1 = $1050. After two years, it would be A = $1000(1 + 0.05)^2 = $1102.50, and so on.
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The interest rate as a fraction
The interest rate is the amount of money paid on top of the original investment, or principal amount, as a fraction or percentage of that original amount.
The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate and t is the time in years that the money is invested for.
For example, if you invest $2,000 for 2 years at a rate of 4.2%, the interest earned is $280.
The formula for compound interest is A=P(1+r)^n, where A is the final amount, P is the principal amount, r is the interest rate and n is the number of times the interest is compounded per year.
For example, if you invest $100 at an annual interest rate of 5% compounded once a year, the balance after 2 years is $110.25.
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Frequently asked questions
The simple interest I on an investment of P dollars at an interest rate of i% for t years is given by I=Prt.
The balance, A, after 2 years is given by A=P(1+r/100)^2.
The value of the investment after 3n years is given by (1+i/100)^n.
The value of the investment after 2n years is given by (1+i/100)^2.
