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

1.75% and 16 times

Explanation:

Compound interest formula:

`\sf A=P(1+(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+(0.07)/(4))^(4 *4)`

`\sf =791.9576107...`

Equivalent interest rate:

`\sf \implies (r)/(n)= (0.07)/(4)=0.0175=1.75 \%`

Number of times compounded:

`\sf \implies nt=4 * 4=16`