Given: Principal Amount (P) = $300
The rate of interest (r) = (3/4) compounded quarterly.
No. quarters in 3 years (n) = 3×4 = 12
To find: The amount for the CD on maturity. Let it will be (A)
Formula: Compound Amount (A) = P [ 1 + (r ÷100)]ⁿ
Now, (A) = P [ 1 + (r ÷100)]ⁿ
or, = $300 [ 1 + (3 ÷400)]¹²
or, = $300 × [ 403 ÷ 400]¹²
or, = $300 × 1.0938069
or, = $ 328.14
Hence, the correct option will be C. $328.14
Answer:
C. $328.14
Step-by-step explanation:
We have been given that you bought a CD for $300 that earns 3% APR and is compounded quarterly. The CD matures in 3 years.
To find the value of CD at maturity, we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest in compounded per year.
t = Time in years.
[tex]3\%=\frac{3}{100}=0.03[/tex]
Substitute the given values:
[tex]A=300(1+\frac{0.03}{4})^{4\cdot 3}[/tex]
[tex]A=300(1+0.0075)^{12}[/tex]
[tex]A=300(1.0075)^{12}[/tex]
[tex]A=300*1.0938068976709831[/tex]
[tex]A=328.14206930129493[/tex]
[tex]A\approx 328.14[/tex]
Therefore, the CD will be worth $328.14 at maturity.
