Question

Kristen opens a bank account that earns $4\%$ intrest each year, compounded once every two years. If she opened the account with k dollars, which of the following expressions represents the total amount in the account after t years?

• A. $k{\left(1.04\right)}^{2t}$
• B. $k{\left(1.04\right)}^{\frac{t}{2}}$
• C. $k{\left(1.08\right)}^t$
• D. $k{\left(1.08\right)}^{\frac{t}{2}}$

Answer 1

The correct option is C $k{\left(1.08\right)}^t$

Principal $P=k$

Time $T=t$ years

Compound interest rate R = 4% per year =0.04 per year

Compounding frequency n = $\frac{1}{2}$, compounded once in two years

Now, amount is:

$A=P{\left(1+\frac{R}{n}\right)}^T$

$=k{\left(1+\frac{0.04}{1/2}\right)}^T$

$=k{\left(1+0.08\right)}^t$

$=k{\left(1.08\right)}^t$

So correct option C