Question

Steven invests $5,270 into a savings account with an interest rate of 5.71% compounded semiannually. Which equation represents the total balance after t years?

1. A = 5270(1+0.0571t)
2. A = 5270(1+0.0571/2)^2t
3. A = 5270(1+0.0571)^t
4. A = 5270(1+2/0.0571)^0.0571t

Answer 1

Answer: 2. A = 5270(1+0.0571/2)^2t

Explanation:

The question for compounded interest is as follows, where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times this rate is applied during the timeframe, and t is the timeframe:

`\displaystyle A = P(1 + (r)/(n) )^(nt)`

We will substitute the known values into the equation to see which of the given equations represents the total balance.

A is unknown, t is unknown, P is $5,270, r is 5.71% / 100 = 0.0571, and n is 2 (semiannually = twice a year).

`\displaystyle A = P(1 + (r)/(n) )^(nt)`

`\displaystyle A = (5,270)(1 + ((0.0571))/(2) )^((2)(t))`

The answer option that represents this is:

2. A = 5270(1+0.0571/2)^2t