If the principal amount is $700, the interest rate is 9%, and the compound interest is $141.36, what is the time period when compounded annually?*1 year2 years3 years4 years

The formula for compound interest is A = P(1 + r/n)^(nt), where:

A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

Given in the problem: P = $700 r = 9A = P + compound interest =$700 + $141.36 =$841.36 We need to find t.

Since the interest is compounded annually, n = 1. So the formula simplifies to A = P(1 + r)^t.

Let's plug the values into the formula and solve for t:

$841.36 =$700(1 + 0.09)^t 1.20194 = (1.09)^t Taking natural log on both sides: ln(1.20194) = t * ln(1.09) t = ln(1.20194) / ln(1.09)

Calculating the above expression gives t approximately equal to 2. Therefore, the time period when compounded annually is 2 years.