Question

Solve all questions accordingly.

Q1. What is the effective annual rate (yield) of 11% compounded monthly?	Format : 48.69
Q2. An interest rate stated as nominal 11% compounded semi-annually  is the same as ? per semi-annual .	Format : 7
Q3. The yield is 8.16 % for a rate compounding semi-annually. Calculate the nominal interest rate.	Format : 7.33
Q4. Meidrim has found her dream house. The house price is RM 360000 and the required downpayment is RM 72000. The loan that Meidrim has decided upon will be for 30 year with annual rate of 8% compunded monthly. Calculate the monthly payment that Meidrim has to pay. Hint: round % and interest factor to 4 decimal points).	Format : 5364.46
Q5. For the RM8600 amount borrowed, the repayment is scheduled to be over 4 year, to be paid monthly. Calculate the remaining unpaid loan after the 6th payment. The interest is 10% compounded monthly.

Answer 1

Solution:

1a) Effective interest rate = (1+ (nominal interest/compounding per period)^(time*compounding per period) -1 =  [(1+(13%/4))^4] - 1 = 13.65%

1b) An interest rate stated as nominal 16% compounded semi-annually is the same as 8% (16%/2) per semi-annual.

1c) Effective interest rate = (1+ (nominal interest/compounding per period)^(time*compounding per period) -1

8.2432% = [(1+ (nominal interest/4)^(4)] -1

1.082432 = (1+ (nominal interest/4)^(4)

(1.02)^4 = (1+ (nominal interest/4)^(4)

(1.02) = (1+ (nominal interest/4)

Nominal interest = 0.08 or 8%

1d) Loan = House price - down payment = $350,000 - $70,000 = $280,000

Monthly payment = Loan x monthly interest x ((1+monthly interest)^total months)/((1+monthly interest)^total months -1)

Monthly payment = RM280,000 x 1% x ((1+1%)^(30x12))/((1+1%)^(30x12) -1)

Monthly payment = RM2,800 x ((1.01)^(360))/((1.01)^(360) -1)

Monthly payment = RM2,880.12

1e) Monthly payment = Loan x monthly interest x ((1+monthly interest)^total months)/((1+monthly interest)^total months -1)

Monthly payment = RM7000 x 0.75% x ((1+0.75%)^(4x12))/((1+0.75%)^(4x12) -1)

Monthly payment = RM52.5 x ((1+0.75%)^(48))/((1+0.75%)^(48) -1)

Monthly payment = RM174

Therefore, monthly payment schedule:

Principle = Balance after precious payment

Interest = Principle*0.75%

Balance = Principle + Interest - EMI

Unpaid loan after the 6th payment = RM6257.19