To find the value of the investment at the end of 10 years for different compounding periods, we will use the formula for compound interest:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial investment), which is $2900.
• $r$ is the annual interest rate (3.2% = 0.032).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the time the money is invested for (10 years).

Let's calculate each case:

(a) 3.2% compounded annually ($n = 1$):

$A = 2900 \left(1 + \frac{0.032}{1}\right)^{1 \times 10}$

(b) 3.2% compounded semiannually ($n = 2$):

$A = 2900 \left(1 + \frac{0.032}{2}\right)^{2 \times 10}$

(c) 3.2% compounded quarterly ($n = 4$):

$A = 2900 \left(1 + \frac{0.032}{4}\right)^{4 \times 10}$

(d) 3.2% compounded monthly ($n = 12$):

$A = 2900 \left(1 + \frac{0.032}{12}\right)^{12 \times 10}$

(e) 3.2% compounded daily ($n = 365$):

$A = 2900 \left(1 + \frac{0.032}{365}\right)^{365 \times 10}$

Now, I'll calculate these values.Here are the values of the investment at the end of 10 years for different compounding frequencies:

(a) 3.2% compounded annually: $3973.70

(b) 3.2% compounded semiannually: $3983.57

(c) 3.2% compounded quarterly: $3988.59

(d) 3.2% compounded monthly: $3991.97

(e) 3.2% compounded daily: $3993.61

Would you like further details or explanations on any of these calculations?

Here are 5 related questions you might find helpful:

1. How does the investment grow with continuous compounding?
2. What happens if the interest rate changes to 4% compounded monthly?
3. How would the values change if the investment period is 20 years instead of 10 years?
4. What is the difference in total interest earned between annual and daily compounding?
5. How do you calculate the compound interest if additional deposits are made regularly?

Tip: Compounding more frequently results in slightly higher returns, but the difference becomes marginal as the compounding frequency increases.