Mr. Ling deposits $250 into a savings account, and his balance after t years is given by

Question

$
250
(
1
+
0.034
4
)
4
t
. Which of these represents the correct interpretation of Mr. Ling's interest rate?

A.
He earns an annual interest rate of 0.85% compounded annually.

B.
He earns an annual interest rate of 3.4% compounded annually.

C.
He earns an annual interest rate of 0.85% compounded quarterly.

D.
He earns an annual interest rate of 3.4% compounded quarterly.

Answer 1

To determine the correct interpretation of Mr. Ling's interest rate, let's analyze the expression given:

\[ 250 \left(1 + \frac{0.034}{4}\right)^{4t} \]

In this expression:

• The term \(0.034\) represents the nominal annual interest rate (3.4%).
• The division by \(4\) indicates that the interest is being compounded quarterly.

So, the formula shows that the interest of 3.4% is being divided into 4 parts (because of quarterly compounding), and thus each quarter, Mr. Ling earns:

\[ \frac{0.034}{4} = 0.0085 = 0.85% \]

Therefore, he earns 0.85% interest per quarter.

Since the nominal annual interest rate is \( 3.4% \), and the compounding is quarterly, the correct answer is:

D. He earns an annual interest rate of 3.4% compounded quarterly.