Question

You invest
$
100
$100 into a CD offering 5% APR with semi-annual compounding (i.e., two times per year).

How much money will you have in the account after 1 year?


125.32
125.32



105.06
105.06



118.54
118.54



120.00
120.00

Answer 1

To calculate the amount of money you will have after 1 year with a principal of $100, an annual percentage rate (APR) of 5%, and semi-annual compounding, we will use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) = the amount of money in the account after t years
- \( P \) = the principal amount (initial investment)
- \( r \) = annual interest rate (decimal)
- \( n \) = number of times interest is compounded per year
- \( t \) = the number of years the money is invested for

Substituting in your values:
- \( P = 100 \)
- \( r = 0.05 \) (5% as a decimal)
- \( n = 2 \) (because interest is compounded semi-annually)
- \( t = 1 \)

Now, we can perform the calculation:

\[
A = 100 \left(1 + \frac{0.05}{2}\right)^{2 \times 1}
\]

\[
A = 100 \left(1 + 0.025\right)^{2}
\]

\[
A = 100 \left(1.025\right)^{2}
\]

\[
A = 100 \times 1.050625
\]

\[
A = 105.06
\]

So, after 1 year, you will have **$105.06** in the account.

Thus, the correct answer is **105.06**.