Question

question 8 of 10 if $5700 is invested in a savings account for which interest is compounded annually, and if the $5700 turns into $6100 in 12 years, what is the interest rate of the savings account? a. 3.45% b. 0.57% c. 1.71% d. 7.02%

Explanation:

Step1: Recall compound interest formula

The formula for annual compound interest is $A = P(1 + r)^t$, where:

• $A = 6100$ (final amount),
• $P = 5700$ (principal),
• $t = 12$ (years),
• $r$ = annual interest rate (unknown).

Step2: Isolate the $(1+r)$ term

Rearrange the formula to solve for $(1+r)$:
$$\frac{A}{P} = (1 + r)^t$$
Substitute values:
$$\frac{6100}{5700} = (1 + r)^{12}$$
Calculate the left-hand side:
$$1.070175 = (1 + r)^{12}$$

Step3: Solve for $(1+r)$

Take the 12th root of both sides:
$$1 + r = 1.070175^{\frac{1}{12}}$$
Calculate the root:
$$1 + r \approx 1.0057$$

Step4: Solve for $r$

Subtract 1 from both sides and convert to percentage:
$$r \approx 1.0057 - 1 = 0.0057 = 0.57\%$$

Answer:

B. 0.57%