Question

You invest $600 in an account that has a annual interest rate of 7%, compounded quarterly for four years. What is the equivalent interest rate, and how many times will the money be compounded?
1.75% and 1 time
5.7% and 4 times
1.75% and 16 times
5.7% and 16 times

Answer 1

Answer:

1.75% and 16 times

Step-by-step explanation:

Compound interest formula:

$\sf A=P(1+\frac{r}{n})^{nt}$

where:

• A = final amount
• P = initial principal balance
• r = annual interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods

Given:

• P = $600
• r = 7% = 0.07
• n = 4
• t = 4

Substituting given values into the formula:

$\sf \implies A=600(1+\frac{0.07}{4})^{4 \times4}$

          $\sf =791.9576107...$

Equivalent interest rate:

$\sf \implies \dfrac{r}{n}= \dfrac{0.07}{4}=0.0175=1.75 \%$

Number of times compounded:

$\sf \implies nt=4 \times 4=16$