Justin invests $10,000 per month for five years at 6.00% annual effective with the first payment made immediately. He used the accumulated value of the investment to purchase a house. If inflation is 3% per year, what is the current value of the house he would purchase assuming houses appreciate at the inflation rate?

Justin

Present value of $714,677.31 at 3% per year for 5 years:

Discount factor of 3% for 5 years (discount factor table) = 0.863

Present value = $714,677.31 x 0.863

= $616,766.52

The house has a current value of $616,766.52.

Explanation:

a) Data and Calculations:

Investment = $10,000 per month

Period = 5 years or 60 months

Annual effective interest = 6% or 0.5% monthly

b) Future value of investment, using an online financial calculator:

FV (Future Value)$714,677.31

PV (Present Value)$529,841.89

N (Number of Periods)60.000

I/Y (Interest Rate)0.500%

PMT (Periodic Payment)$10,000.00

Starting Investment$10,000.00

Total Principal$610,000.00

Total Interest$104,677.31

c) First, we work out the future value of Justin's investment of $10,000 per month for five years at 6% annual effective.  This gives us a future value of $714,677.31.  Then, we can discount this future value to its present value with a discount factor of 0.863 if the inflation rate is 3% becauses houses appreciate at the inflation rate.  Multiplying this future value by the discount factor gives the present value of the house as $616,766.52.  This means that the house had appreciated in value by $97,910.79 at the inflation rate of 3% per year after five years.

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