To determine the value of the account after 10 years with changing interest rates and compounding frequencies, we will break the problem into two parts:

1. First 5 years: Interest rate of 7% compounded semiannually.
2. Next 5 years: Interest rate increases to 7.08% compounded quarterly.

Part 1: First 5 Years

The formula for compound interest is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

• $A$ = final amount
• $P$ = initial principal (starting with $1000)
• $r$ = annual interest rate (7% or 0.07)
• $n$ = number of times interest is compounded per year (semiannually = 2)
• $t$ = number of years (5 years)

Substitute the values: $A_1 = 1000 \left(1 + \frac{0.07}{2}\right)^{2 \times 5}$

Part 2: Next 5 Years

Now, after the first 5 years, the interest rate changes to 7.08% compounded quarterly. We use the same formula, but this time:

• The new principal is the amount $A_1$ obtained after 5 years.
• $r = 0.0708$
• $n = 4$ (compounded quarterly)
• $t = 5$ (for the next 5 years)

The new formula for the second period is: $A_2 = A_1 \left(1 + \frac{0.0708}{4}\right)^{4 \times 5}$

Let me calculate the final amount.The value of the account after a total of 10 years will be $2004, rounded to the nearest dollar.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How does the frequency of compounding affect the final amount?
2. What would the value be if the interest rate remained at 7% for the entire 10 years?
3. How would the value change if interest was compounded annually instead of semiannually?
4. What is the impact of increasing the interest rate slightly, as in the second period of this example?
5. How can you calculate the effective annual rate (EAR) for the given interest rates?

Tip: The more frequently interest is compounded, the higher the final account value will be. This is due to interest being applied more often within the same time frame.