You want to buy a small house that costs RM100,000. You have RM10,000 for a down payment and repaid in equal installments at the end of each of the next 3 years. The interest rate is 7 percent compounded annually.

a. Calculate how much you need to pay for each year. b. Set up an amortization schedule for the loan.

To calculate how much you need to pay for each year, you can use the formula for the periodic payment amount on a loan. The formula is:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:
P = periodic payment amount
r = interest rate per period
PV = present value or loan amount
n = total number of periods

In this case, the loan amount (PV) is RM100,000, the interest rate (r) is 7 percent (or 0.07), and the total number of periods (n) is 3 years.

a. Calculating the payment for each year:
First, we need to calculate the interest rate per period. Since it's compounded annually, we need to convert the annual rate to a per-period rate.
r = 0.07 / 1 = 0.07

For the first year:
P1 = (0.07 * 100,000) / (1 - (1 + 0.07)^(-3))
P1 ≈ RM38,356.73

For the second year:
P2 = (0.07 * 100,000) / (1 - (1 + 0.07)^(-2))
P2 ≈ RM38,356.73

For the third year:
P3 = (0.07 * 100,000) / (1 - (1 + 0.07)^(-1))
P3 ≈ RM38,356.73

So, you would need to pay approximately RM38,356.73 for each year.

b. Setting up an amortization schedule:
An amortization schedule provides a detailed breakdown of each payment, including the amount applied to principal and interest.

Here's an example of an amortization schedule for this loan:

Year Principal Payment Interest Payment Total Payment Remaining Balance
Year 1 RM10,000 RM28,356.73 RM38,356.73 RM61,643.27
Year 2 RM16,643.27 RM21,713.46 RM38,356.73 RM44,929.81
Year 3 RM23,374.03 RM15,982.70 RM38,356.73 RM21,555.78

The remaining balance is updated each year, and the interest payment decreases while the principal payment increases as the loan gets paid down.

Note: The numbers in the amortization schedule might vary slightly due to rounding.