Question

Suppose you buy a CD for $300 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity? A. $309.12 B. $309.10 C. $328.14 D. $303.01

Answer 1

C. $328.14

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.

`A=P(1+(r)/(n))^(n\cdot t)`, 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.

`3\%=(3)/(100)=0.03`

Substitute the given values:

`A=300(1+(0.03)/(4))^(4\cdot 3)`

`A=300(1+0.0075)^(12)`

`A=300(1.0075)^(12)`

`A=300*1.0938068976709831`

`A=328.14206930129493`

`A\approx 328.14`

Therefore, the CD will be worth $328.14 at maturity.

Answer 2

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