To determine the future value of the certificate of deposit (CD), you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = future value
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Based on the information provided:
P = $4,000
r = 6% (0.06)
n = 12 (compounded monthly)
t = 6 months (since it's a 6-month CD)
a. What would be the future value of the CD at the end of the investment term?
Using the formula, we can calculate:
A = $4,000(1 + 0.06/12)^(12*0.5)
A = $4,000(1 + 0.005)^(6)
A = $4,000(1.005)^6
A ≈ $4,000(1.0304)
A ≈ $4,121.60
Therefore, the future value of the CD at the end of the 6-month investment term would be approximately $4,121.60.
b. How much interest would the investment earn for the period?
To calculate the interest earned, you can subtract the initial investment from the future value:
Interest = Future Value - Principal
Interest = $4,121.60 - $4,000
Interest ≈ $121.60
Therefore, the investment would earn approximately $121.60 in interest for the 6-month period.
c. What would be the effective rate of the investment?
The effective rate takes into account the compounding frequency and provides an annualized rate for comparison purposes. It can be calculated using the following formula:
Effective Rate = (1 + r/n)^n - 1
For the CD investment:
r = 6% (0.06)
n = 12 (compounded monthly)
Using the formula, we can calculate:
Effective Rate = (1 + 0.06/12)^12 - 1
Effective Rate ≈ (1 + 0.005)^12 - 1
Effective Rate ≈ (1.005)^12 - 1
Effective Rate ≈ 0.061678 - 1
Effective Rate ≈ 0.061678
Therefore, the effective rate of the CD investment would be approximately 6.17%.