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.
