Answer to Question #100622 in Financial Math for JANNATUL NAIMMAH ISMADI

Question

1. You have two options in accumulating your wealth:-
Option 1: depositing amounts of RM P at the end of every month for 25 years at an annual effective rate of dividend of 10%.
Option 2: Purchasing a house by loan amounting RM 200,000 for 25 years with a nominal rate of interest 4.5% compounded monthly. The loan is paid in monthly level payments. The house value is increasing at yield of 5% per year. Immediately after purchasing the house, you are making money by renting your house at RM550 per month earning at the beginning of the month until the housing loan has been paid. Your level monthly renting house are to be reinvested at dividend rate of 9% per annual. At the end of 25 years, you wish to sell back your house based on the yield rate of your house.
Based on the above information, evaluate which of the investment method above is better. Explain.

Answer 1

Option 2 loan monthly payment is:

$MP = 200,000×(0.045/12)×\frac{(1 + 0.045/12)^{25×12}}{((1 + 0.045/12)^{300} - 1)} = 1,111.66.$

The total amount to be paid is:

1,111.66×12×25 = 333,500.

The accumulated rent is:

$A = 550×\frac{(1 + 0.09/12)^{300} - 1)} {0.09/12} = 616,617.07.$

The house value in 25 years is:

200,000×1.05^25 = 677,271.

So, the total gain in 25 years is:

677,271 + 616,617.07 - 333,500 = 960,388.07.

Option 1 will gain:

$A = 1,111.66×\frac{(1 + 0.1/12)^{300} - 1)} {0.1/12} = 1,608,266.82.$

So, the option 1 is better.