Answer:
Nicholas will have earned $1.5 interest after the 1st quarter ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- Nicholas wants to buy a CD for $200
- It earns 3% APR and is compounded quarterly
- The CD matures in 5 years
- Nicholas will be paid the interest he earns each quarter
- The rule of the compounded interest = [tex]P(1+\frac{r}{n})^{nt}-p[/tex]
where:
# P = the principal investment amount
# r = the annual interest rate in decimal
# n = the number of times that interest is compounded per unit t
# t = the time the money is invested for
∵ P = $200
∵ r = 3/100 = 0.03
∵ n = 4 ⇒ compounded quarterly
- We want to find the interest Nicholas will have earned on this CD
after the first quarter
∴ t = 1/4 year
∴ The interest = [tex]200(1+\frac{0.03}{4})^{4(\frac{1}{4})}-200=1.5[/tex]
* Nicholas will have earned $1.5 interest after the 1st quarter
