What is the profit for Mr. Lee\'s investment? Here is the story: In January, 200

Question

What is the profit for Mr. Lee's investment?

Here is the story:

In January, 2006, Mr. Lee purchased a co-op in Miami. The price is $200,000. Down payment is 10%. Mortage rate is 4.25% for 30 years. Saving rate is 0.3% per year. Maintains fee is $589 per month. Rent income is $1,450/month. If inflation rate is 5% per year and we assume the price of the apartment will increase at the same inflation rate. What is the investment return for Mr. Lee's investment in January, 2036?

1. What is the monthly payment for this mortgage?

2. How much does Mr. Lee have to pay every month?

3. What is the value of this saving after 30 years?

4. What is the house price after 30 years?

5. What is the investment return?

Explanation / Answer

(1)

Monthly payment = Loan amount x [r x (1 + r)N] / [(1 + r)N - 1]

Here, r = 4.25% per year / 12 = 0.35% per month

N = 30 x 12 = 360 months

Loan amount = $200,000 x 90% = $180,000

Monthly payment = $180,000 x [0.0035 x (1.0035)360] / [(1.0035)360 - 1]

= $180,000 x 0.0123 / 2.5177

= $879.37

(2)

Monthly payment to be made = Mortgage payment + Maintenance fee - Rental income

= $(879.37 + 589 - 1,450)

= $18.37

(3)

Monthly savings rate = 0.3% / 12 = 0.025%

Value of this saving after 30 years = $18.37 x Future value interest factor of annuity (0.025%, 360 months)

= $18.37 x [(1 + r)N - 1] / r

= $18.37 x [(1.00025)360 - 1] / 0.00025

= $6,919

(4)

House price after 30 years = $200,000 x (1.05)30 = $200,000 x 4.3219 = $864,380

(5)

Future value of down payment of $20,000 = $20,000 x (1.05)30 = $86,438.85

Investment return (Nominal rate) = [Future value of Home price - Future value of Down payment - Future value of monthly payments made] / [Future value of Down payment - Future value of monthly payments made]

= $[864,380 - 86,438.85 - 6,919] / $[86,438.85 + 6,919] x 100

= 8.26 x 100

= 826%

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