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[SOWHAT0819]

Determine the future amount of P100for 10 1/4 years at the rate of 5% compounded:
a.Monthly
b. Quarterly
c. Annually
d. Semi-annually
e.Daily

 

[🤖]

To determine the future amount of P100 for 10 1/4 years at a 5% interest rate compounded at different frequencies, we can use the compound interest formula:

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

Where:

• \( A \) is the future amount
• \( P = 100 \) is the principal amount
• \( r = 0.05 \) is the annual interest rate
• \( t = 10\frac{1}{4} = 10.25 \) years

Let's calculate the future amounts for each compounding frequency:

a. Monthly compounding:
\[ A = 100 \left(1 + \frac{0.05}{12}\right)^{12 \times 10.25} \]
\[ A = 100 \left(1 + \frac{0.05}{12}\right)^{123} \]
\[ A \approx 100 \times 1.6488 \]
\[ A \approx 164.88 \]

b. Quarterly compounding:
\[ A = 100 \left(1 + \frac{0.05}{4}\right)^{4 \times 10.25} \]
\[ A = 100 \left(1 + 0.0125\right)^{41} \]
\[ A \approx 100 \times 1.6470 \]
\[ A \approx 164.70 \]

c. Annually compounding:
\[ A = 100 \times (1 + 0.05)^{10.25} \]
\[ A = 100 \times 1.6289 \]
\[ A \approx 162.89 \]

d. Semi-annually compounding:
\[ A = 100 \times (1 + 0.025)^{2 \times 10.25} \]
\[ A = 100 \times 1.6398 \]
\[ A \approx 163.98 \]

e. Daily compounding:
\[ A = 100 \left(1 + \frac{0.05}{365}\right)^{365 \times 10.25} \]
\[ A = 100 \left(1 + \frac{0.05}{365}\right)^{3746.25} \]
\[ A \approx 100 \times 1.6513 \]
\[ A \approx 165.13 \]

Therefore, the future amounts of P100 at different compounding frequencies are approximately:
a. Monthly: P164.88
b. Quarterly: P164.70
c. Annually: P162.89
d. Semi-annually: P163.98
e. Daily: P165.13