Answer :

To calculate the final amount for a $10,000 CD at 4.50% interest for 4 years compounded quarterly, we'll use the compound interest formula:

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

Where:

- A is the amount of money accumulated after n years, including interest.

- P is the principal amount (the initial amount of money).

- r is the annual interest rate (in decimal).

- n is the number of times that interest is compounded per year.

- t is the time the money is invested for in years.

Given:

- Principal amount (P) = $10,000

- Annual interest rate (r) = 4.50% = 0.045

- Compounding frequency (n) = Quarterly

- Time (t) = 4 years

Now, let's plug these values into the formula:

[ A = 10000left(1 + frac{0.045}{4}right)^{4 times 4} ]

Let's calculate:

[ A = 10000left(1 + frac{0.045}{4}right)^{16} ]

[ A = 10000left(1 + frac{0.01125}{1}right)^{16} ]

[ A = 10000(1.01125)^{16} ]

[ A ≈ 10000(1.193435318) ]

[ A ≈ 11934.35 ]

So, at the end of 4 years compounded quarterly, the amount in the certificate of deposit would be approximately $11,934.35.