The problem asks to calculate the compound interest and total amount after 5 years for an investment of Tk. 1,00,000 at a 10% interest rate, compounded monthly and quarterly respectively.

1. Problem Description

The problem asks to calculate the compound interest and total amount after 5 years for an investment of Tk. 1,00,000 at a 10% interest rate, compounded monthly and quarterly respectively.

2. Solution Steps

(i) Monthly Compounding:

The formula for compound interest is:

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

Where:

$A$ = the future value of the investment/loan, including interest

$P$ = the principal investment amount (the initial deposit or loan amount)

$r$ = the annual interest rate (as a decimal)

$n$ = the number of times that interest is compounded per year

$t$ = the number of years the money is invested or borrowed for

In this case:

$P = 1,00,000$

$r = 0.10$

$n = 12$ (monthly compounding)

$t = 5$

$A = 1,00,000(1 + \frac{0.10}{12})^{(12*5)}$

$A = 1,00,000(1 + 0.008333)^{(60)}$

$A = 1,00,000(1.008333)^{60}$

$A = 1,00,000 * 1.645309$

$A = 1,64,530.90$

Compound Interest = $A - P$

Compound Interest = $1,64,530.90 - 1,00,000$

Compound Interest = $64,530.90$

(ii) Quarterly Compounding:

Using the same formula, with:

$P = 1,00,000$

$r = 0.10$

$n = 4$ (quarterly compounding)

$t = 5$

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

$A = 1,00,000(1 + \frac{0.10}{4})^{(4*5)}$

$A = 1,00,000(1 + 0.025)^{20}$

$A = 1,00,000(1.025)^{20}$

$A = 1,00,000 * 1.638616$

$A = 1,63,861.60$

Compound Interest = $A - P$

Compound Interest = $1,63,861.60 - 1,00,000$

Compound Interest = $63,861.60$

3. Final Answer

(i) Monthly Compounding:

Total Amount = Tk. 1,64,530.90

Compound Interest = Tk. 64,530.90

(ii) Quarterly Compounding:

Total Amount = Tk. 1,63,861.60

Compound Interest = Tk. 63,861.60