Question

Suzy has $4,066 to invest in a simple interest account. She hopes to gain $1,393 in interest after 9 years. What annual percentage rate does she need to find to make sure she earns this much interest? Leave the answer as a decimal, rounded to 4 decimal places.

a. 0.0346
b. 0.0497
c. 0.0678
d. 0.0932

Answer 1

To calculate the annual percentage rate Suzy needs to earn $1,393 in interest over 9 years, we use the simple interest formula. After solving the formula, we find that Suzy needs an annual rate of approximately 0.0381, or 3.81%, which is option (a).

Step-by-step explanation:

To find the annual percentage rate (APR) that Suzy needs to invest her $4,066 to gain $1,393 in interest after 9 years, we use the formula for simple interest I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest per year, and T is the time in years.

Substituting the given values we have I = $1,393, P = $4,066, T = 9. We need to solve for R.

So: $1,393 = $4,066 × R × 9

Now, to solve for R

R = $1,393 / ($4,066 × 9)

R = $1,393 / $36,594

R ≈ 0.03806

Rounded to four decimal places, R = 0.0381

So, the annual percentage rate that Suzy needs to find is approximately 0.0381, or 3.81%, which is closest to option a. 0.0346 when rounded to four decimal places.