Question

Emile wants to buy a house. Today the price of the house is $500000, but because of inflation the price increases 1% per year. Emile has an investment account where he earns 7% compounded annually. Currently, Emile has $250000 in his account. Give all of your answers to 2 decimal places, including the number of years; assume the Theoretical Method for computing A(t) for fractional periods (years).

a) How many years until Emile has (at least) today's price of the house in his account?    

Write the equation you used to compute this answer:

b) What is the new price of the house at that time?  

c) What is the "real" (or "inflation adjusted") rate of return on Emile's account?    (To 2 decimals. Write 3.06% as 3.06 not 0.036.)

d) Using the real rate of return from c), how long until Emile's account grows from its initial balance to (at least) today's price of the house?    

e) Using your answer from d) how much money does Emile have in his account (using his actual rate of return)?    (2 decimal places)

f) Using your answer from d), what is the price of the house at that time?  

g) Emile has exactly enough money to buy the house at this later time?   True/False

Answer 1

Solution:

a)Calculation of no. of year

We know that,

Future Value=Present Value(1+interest rate)^no. of years

$500,000=$250,000*(1+0.07)^no.of years

(1.07)^no. of years=2

No. of years=11 years

Thus it will take 11 years until  Emile has (at least) today's price of the house in his account.

b)Calculation of new price of the house

New price of the house=Current Price(1+Inflation rate)^no. of years

=$500,0000(1+0.01)^11

=$557,834.17

c)Real Rate of return=Nominal Interest rate-Inflation rate of return

=7%-1%=6%

d)Using real rate of return,calcualtion of no. of years

Future value=Present value(1+real rate of return)^no. of years

$500,000/$250,000=(1+0.06)^no. of years

No. of years=12 years

Thus it will take 12 years until  Emile has (at least) today's price of the house in his account