Answer:
a) Quarterly Compound Interest
b) Rs 243101.25
c) Rs 243390.7424
Step-by-step explanation:
Part a:
Let's calculate the compound interest for each option:
Annual Compound Interest:
The formula for compound interest is given by:
[tex] \sf A = P \left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
where:
- [tex] \sf A[/tex] is the amount after time [tex] \sf t[/tex],
- [tex] \sf P[/tex] is the principal amount,
- [tex] \sf r[/tex] is the annual interest rate (as a decimal),
- [tex] \sf n[/tex] is the number of times interest is compounded per year,
- [tex] \sf t[/tex] is the time in years.
For annual compounding:
[tex] \sf A = 200,000 \left(1 + \dfrac{0.10}{1}\right)^{1 \times 2} \\\\ \sf = Rs \, 242000 [/tex]
Semi-annual Compound Interest:
For semi-annual compounding ([tex] \sf n = 2[/tex]):
[tex] \sf A = 200,000 \left(1 + \dfrac{0.10}{2}\right)^{2 \times 2} \\\\ \sf = Rs \, 243101.25 [/tex]
Quarterly Compound Interest:
For quarterly compounding ([tex] \sf n = 4[/tex]):
[tex] \sf A = 200,000 \left(1 + \dfrac{0.10}{4}\right)^{4 \times 2} \\\\ \sf = Rs \, 24368.05795 [/tex]
Since Rs 24368.05795 is the greatest compound interest. So, Quarterly Compound Interest helps Bipin to get more interest.
[tex]\hrulefill [/tex]
Part (b)
Semi-annual Compound Interest:
For semi-annual compounding ([tex] \sf n = 2[/tex]):
[tex] \sf A = 200,000 \left(1 + \dfrac{0.10}{2}\right)^{2 \times 2} \\\\ \sf = Rs \, 243101.25 [/tex]
He receives Rs 243101.25 after 2 years from interest compounded semi-annually.
[tex]\hrulefill[/tex]
Part (c)
Amount after 1 year with semi-annual compounding:
[tex]\sf A_1 = P \left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
[tex]\sf A_1 = 200,000 \left(1 + \dfrac{0.10}{2}\right)^{2 \times 1} \\\\ \sf \approx Rs \, 220500[/tex]
Amount at the end of the remaining 1 year with quarterly compounding:
[tex]\sf A_2 = P \left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]\sf A_2 = 220500 \left(1 + \frac{0.10}{4}\right)^{4 \times 1} \\\\ \approx Rs \, 243390.7424 [/tex]
Therefore, at the end of 1 year, if Bipin withdraws the total amount received according to the semi-annual compound interest and deposits it for the rest of the period to get quarterly compound interest, he will get approximately Rs 243390.7424.
