Suppose you invest $2250 in a CD that earns 3% APR and is compounded quarterly. The CD matures in 2 years. How much will this CD be worth at maturity?
Suppose you invest $2250 in a CD that earns 3% APR and is compounded quarterly. The CD matures in 2 years. How much will this CD be worth at maturity?
To calculate the future value of the CD at maturity, you can use the formula for compound interest:
Future Value = Principal * (1 + interest rate / number of compounding periods)^(number of compounding periods * number of years)
In this case:
Principal = $2250
Interest rate = 3% or 0.03 (decimal form)
Number of compounding periods = quarters per year = 4
Number of years = 2
Plugging these values into the formula:
Future Value = $2250 * (1 + 0.03 / 4)^(4 * 2)
First, calculate the amount inside the parentheses:
(1 + 0.03 / 4) = (1.0075)
Next, raise this value to the power:
(1.0075)^(4 * 2) = (1.0075)^8 ≈ 1.061678809
Finally, multiply this value by the principal:
Future Value = $2250 * 1.061678809 = $2391.27
Therefore, the CD will be worth approximately $2391.27 at maturity.
To calculate the amount the CD will be worth at maturity, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount at maturity
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $2250
r = 3% = 0.03 (in decimal form)
n = 4 (compounded quarterly)
t = 2 years
Plugging in the values into the formula:
A = $2250(1 + 0.03/4)^(4*2)
A = $2250(1 + 0.0075)^8
A = $2250(1.0075)^8
A ≈ $2397.81
Therefore, the CD will be worth approximately $2397.81 at maturity.