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Nicholas wants to buy a CD for $200 that earns 3% APR and is compounded quarterly. The CD matures in 5 years. He will be paid the interest he earns each quarter. How much interest will Nicholas have earned on this CD after the first quarter?

A. $3.00


B. $6.00


C. $1.50


D. $0.75

2 Answers

2 votes

Answer:

1.50 famo

Explanation:

User Ekans
by
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5 votes

Answer:

Nicholas will have earned $1.5 interest after the 1st quarter ⇒ answer C

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 =
P(1+(r)/(n))^(nt)-p

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 =
200(1+(0.03)/(4))^{4((1)/(4))}-200=1.5

* Nicholas will have earned $1.5 interest after the 1st quarter

User Aleix CC
by
4.6k points