To calculate the final amount for each case in the table, we will use the compound interest formula:

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

Where:

• $A$: Final amount (including principal and interest)
• $P$: Principal (initial investment)
• $r$: Annual nominal interest rate (as a decimal)
• $n$: Number of compounding periods per year
• $t$: Time in years

Let’s solve for each part:

a) $300 at 2.3% compounded semi-annually for 18 months

• P = 300
• r = $2.3\% = 0.023$
• n = 2 (semi-annually)
• t = $18 \, \text{months} = 1.5 \, \text{years}$

$A = 300 \left(1 + \frac{0.023}{2}\right)^{2 \cdot 1.5}$

b) $1200 at 1.25% compounded weekly for 2 years

• P = 1200
• r = $1.25\% = 0.0125$
• n = 52 (weekly compounding)
• t = 2 years

$A = 1200 \left(1 + \frac{0.0125}{52}\right)^{52 \cdot 2}$

c) $1575 at 0.75% compounded daily for 85 days

• P = 1575
• r = $0.75\% = 0.0075$
• n = 365 (daily compounding)
• t = $\frac{85}{365} \approx 0.2329 \, \text{years}$

$A = 1575 \left(1 + \frac{0.0075}{365}\right)^{365 \cdot 0.2329}$

d) $870 at 18% compounded quarterly for 3.5 years

• P = 870
• r = $18\% = 0.18$
• n = 4 (quarterly compounding)
• t = 3.5 years

$A = 870 \left(1 + \frac{0.18}{4}\right)^{4 \cdot 3.5}$

e) $14000 at 5.45% compounded annually for 9 months

• P = 14000
• r = $5.45\% = 0.0545$
• n = 1 (annual compounding)
• t = $9 \, \text{months} = 0.75 \, \text{years}$

$A = 14000 \left(1 + \frac{0.0545}{1}\right)^{1 \cdot 0.75}$

Let me calculate these results now. Constants for the calculations from math import pow

Function to calculate compound interest

def compound_interest(P, r, n, t): return P * pow((1 + r / n), n * t)

Input values for each case

Case a

P_a, r_a, n_a, t_a = 300, 0.023, 2, 1.5

Case b

P_b, r_b, n_b, t_b = 1200, 0.0125, 52, 2

Case c

P_c, r_c, n_c, t_c = 1575, 0.0075, 365, 85 / 365

Case d

P_d, r_d, n_d, t_d = 870, 0.18, 4, 3.5

Case e

P_e, r_e, n_e, t_e = 14000, 0.0545, 1, 0.75

Calculating the amounts

A_a = compound_interest(P_a, r_a, n_a, t_a) A_b = compound_interest(P_b, r_b, n_b, t_b) A_c = compound_interest(P_c, r_c, n_c, t_c) A_d = compound_interest(P_d, r_d, n_d, t_d) A_e = compound_interest(P_e, r_e, n_e, t_e)

Rounding results to 2 decimal places

A_a, A_b, A_c, A_d, A_e = round(A_a, 2), round(A_b, 2), round(A_c, 2), round(A_d, 2), round(A_e, 2)

A_a, A_b, A_c, A_d, A_eHere are the calculated amounts for each case:

1. a) Final Amount = $310.47
2. b) Final Amount = $1230.37
3. c) Final Amount = $1577.75
4. d) Final Amount = $1611.19
5. e) Final Amount = $14568.44

Do you need me to explain any step in detail or verify any specific value?

Related Questions:

1. How is the compound interest formula derived?
2. What is the difference between simple interest and compound interest?
3. How does compounding frequency affect the final amount?
4. How would these values change if the interest rate was doubled?
5. How can the effective interest rate be calculated for these scenarios?

Tip:

The higher the compounding frequency (e.g., daily vs annually), the greater the final amount due to the interest-on-interest effect.