A hospital administrator places \12,000 into a fixed-term savings certificate that earns a… — Armed Services Vocational Aptitude Battery (ASVAB)

A hospital administrator places $\$12,000$ into a fixed-term savings certificate that earns an annual simple interest rate of $4.2\%$ . If no other deposits or withdrawals are made, what is the total accumulated balance, in dollars, of the certificate after exactly 30 months?

Answer: 13260

Answer

The total accumulated balance is 13260.

The correct answer is found by first converting the 30-month time period into 2.5 years (

30 \div 12 = 2.5

), and the

4.2\%

interest rate into the decimal

0.042

(

4.2 \div 100 = 0.042

). Using the simple interest formula

I = P \times R \times T

, the interest earned is

\$12,000 \times 0.042 \times 2.5 = \$1,260

. Adding this interest to the original principal of

\$12,000

gives a total accumulated balance of

\$13,260

Step-by-Step Solution

Convert the interest rate to a decimal and the time period to years.

R = 4.2\% = 0.042

, and

T = 30 \text{ months} \div 12 \text{ months/year} = 2.5 \text{ years}

The standard simple interest formula requires the interest rate as a decimal and the time expressed in years.

Calculate the total interest earned using the simple interest formula

I = P \times R \times T

I = 12000 \times 0.042 \times 2.5 = 1260

This determines how much additional money the certificate earns over the 30-month period.

Calculate the total accumulated balance by adding the interest earned to the original principal.

Total Balance =

12000 + 1260 = 13260

The question asks for the total accumulated balance, which includes both the initial deposit (principal) and the earned interest.

Key Concept

Calculating simple interest over a fractional year and determining the total accumulated amount.

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