To find out how much money you will have at the end of the term with the given conditions, we can use the formula for compound interest:
[ A = P(1 + frac{r}{n})^{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) = 5.75% = 0.0575
- Compounding frequency (n) = Monthly
- Time (t) = 1 year (since it's compounded monthly, it's for 1 year)
Now, let's plug these values into the formula:
[ A = 10000left(1 + frac{0.0575}{12}right)^{12 times 1} ]
Let's calculate:
[ A = 10000left(1 + frac{0.0575}{12}right)^{12} ]
[ A = 10000left(1 + frac{0.0575}{12}right)^{12} ]
[ A = 10000left(1 + frac{0.00479167}{12}right)^{12} ]
[ A = 10000left(1 + 0.000399305right)^{12} ]
[ A = 10000(1.000399305)^{12} ]
[ A ≈ 10000(1.06095) ]
[ A ≈ 10609.50 ]
So, at the end of 1 year, the amount in the certificate of deposit would be approximately $10,609.50.
