Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?
2000 * 1.065^10
213
To calculate the amount you will have when the CD matures, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $2,000, the annual interest rate (r) is 6.5% (or 0.065 as a decimal), the compound frequency (n) is 1 (compounded annually), and the number of years (t) is 10.
Plugging these values into the formula:
A = 2000(1 + 0.065/1)^(1*10)
Simplifying the equation:
A = 2000(1 + 0.065)^10
Evaluating the expression inside the parentheses:
A = 2000(1.065)^10
Calculating the exponent:
A = 2000(1.790847)
Multiplying the principal amount by the result:
A ≈ $3,581.69
Therefore, when the CD matures, you will have approximately $3,581.69.
To calculate how much you will have when the CD matures, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $2,000 (principal amount)
r = 6.5% (annual interest rate = 0.065)
n = 1 (compounded annually)
t = 10 years
Now, let's plug these values into the formula and calculate the future value:
A = $2,000(1 + 0.065/1)^(1*10)
A = $2,000(1 + 0.065)^10
A = $2,000(1.065)^10
A ≈ $2,000(1.790847)
A ≈ $3,581.69
Therefore, when the CD matures in 10 years, you will have approximately $3,581.69.