The value of the certificate of deposit after 10 years can be calculated using the formula for compound interest:

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

Where:

• $A$ = the amount of money accumulated after $t$ years, including interest
• $P$ = the principal amount (initial deposit) = $5,000
• $r$ = annual interest rate (in decimal) = 7% = 0.07
• $n$ = number of times the interest is compounded per year = 12 (monthly compounding)
• $t$ = the number of years = 10

Let's calculate $A$.The certificate will be worth approximately $10,048.31 after 10 years, rounded to the nearest cent.

Do you need further details or have any questions?

Here are five related questions for further practice:

1. What would the value be after 15 years with the same interest rate?
2. How would the value change if the interest were compounded quarterly instead of monthly?
3. What would the certificate be worth if the interest rate were 5% instead of 7%?
4. How much interest would Tara earn in total over the 10 years?
5. How much would need to be deposited initially to have $15,000 after 10 years at the same interest rate?

Tip: The more frequently interest is compounded, the greater the final amount will be due to the effects of compounding interest!