Determine the missing interest rate and the final maturity value. Fill in the blanks with … — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the missing interest rate and the final maturity value. Fill in the blanks with the correct numeric values.

Answer:A municipal worker invests

\\

5,000

into a fixed-rate savings certificate. The certificate pays an annual simple interest rate of 【3.75】

\\%

. After

years, the certificate has earned

750

in interest, bringing the total maturity value to

\\

【5750】$.

The annual simple interest rate is 3.75% and the total maturity value is $5,750.

The missing interest rate is found by rearranging the formula

I = PRT

to solve for rate:

R = \frac{I}{PT}

. Dividing the interest (

\$750

) by the product of the principal (

\$5,000

) and the time (

4

years) gives a decimal of

0.0375

, which is

3.75\\%

. The total maturity value is simply the initial principal (

\$5,000

) plus the interest earned (

\$750

), which equals

\\

5,750$.

Identify the given values for the simple interest formula.

Principal (

P

) =

\\

5,000

, Interest (

) =

750

, Time (

T

) =

4

years.

To find the missing annual interest rate, we must first list the known values for the formula

I = PRT

Substitute the known values into the simple interest formula and solve for the rate (

R

750 = 5000 \times R \times 4 \Rightarrow 750 = 20000 \times R \Rightarrow R = \frac{750}{20000} = 0.0375

. Converting this decimal to a percentage gives

3.75\\%

Isolating

R

allows us to determine the annual percentage rate required to earn the specified interest.

Calculate the total maturity value (

A

) by adding the interest earned to the original principal.

A = P + I \Rightarrow A = 5000 + 750 = 5750

The total balance at maturity is the sum of the initial investment and the accumulated interest.

Simple Interest Applications

Question