The problem asks to calculate the equal annual installment payments required to repay a loan of Tk. 42,000 over 8 years, given an interest rate of 12% for the borrower and an 8% return for the lender. We also need to prepare an amortization schedule. Since the loan is provided at 12% interest, but the lender needs an 8% return, this is likely a typo, and we should proceed based on 12%. Let's assume that the question meant that the loan was taken at 8%.

1. Problem Description

The problem asks to calculate the equal annual installment payments required to repay a loan of Tk. 42,000 over 8 years, given an interest rate of 12% for the borrower and an 8% return for the lender. We also need to prepare an amortization schedule. Since the loan is provided at 12% interest, but the lender needs an 8% return, this is likely a typo, and we should proceed based on 12%. Let's assume that the question meant that the loan was taken at 8%.

2. Solution Steps

First, calculate the annual installment payment using the present value of an annuity formula:

$PV = PMT * \frac{1 - (1 + r)^{-n}}{r}$

Where:

$PV$ = Present Value of the loan = Tk. 42,000

$PMT$ = Periodic Payment (Annual Installment) - this is what we need to find

$r$ = Interest rate per period = 8% or 0.08

$n$ = Number of periods = 8 years

Rearrange the formula to solve for $PMT$:

$PMT = \frac{PV * r}{1 - (1 + r)^{-n}}$

Plug in the values:

$PMT = \frac{42000 * 0.08}{1 - (1 + 0.08)^{-8}}$

$PMT = \frac{3360}{1 - (1.08)^{-8}}$

$PMT = \frac{3360}{1 - 0.540269}$

$PMT = \frac{3360}{0.459731}$

$PMT = 7308.54$

Now we will prepare the amortization schedule:

Year | Beginning Balance | Payment | Interest | Principal | Ending Balance

------- | -------- | -------- | -------- | -------- | --------

0 | 42,000.00 | | | | 42,000.00

1 | 42,000.00 | 7,308.54 | 3,360.00 | 3,948.54 | 38,051.46

2 | 38,051.46 | 7,308.54 | 3,044.12 | 4,264.42 | 33,787.04

3 | 33,787.04 | 7,308.54 | 2,702.96 | 4,605.58 | 29,181.46

4 | 29,181.46 | 7,308.54 | 2,334.52 | 4,974.02 | 24,207.44

5 | 24,207.44 | 7,308.54 | 1,936.60 | 5,371.94 | 18,835.50

6 | 18,835.50 | 7,308.54 | 1,506.84 | 5,801.70 | 13,033.80

7 | 13,033.80 | 7,308.54 | 1,042.70 | 6,265.84 | 6,767.96

8 | 6,767.96 | 7,308.54 | 541.44 | 6,767.10 | 0.86

The ending balance for year 8 is slightly off from zero. This is due to rounding errors.

3. Final Answer

The amount of each installment is approximately Tk. 7,308.

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4. The amortization schedule is shown above.