Hello, magentarita!

This is a messy one!

The price of the house is now $500,000.Joe wants to buy a house but does not want to get a loan.

The average price of the dream house is $500,000 and its price is growing at 5% per year.

How much should Joe invest in a project at the end of each year for the next 5 years in order

to accumulate enough money to buy his dream house with cash at the end of the 5th year?

Assume the project pays 12% rate of return.

Its price is increasing by 5% per year.

In five years, its price will be: .

This is the amount he wants to have at the end of five years.

Let's walk through his investment plan.

At the end of year 1, he invests dollars.

By the end of year 2, it has grown to dollars

. . and he deposits another dollars.

He has dollars in his account.

By the end of year 3, it has grown to dollars

. . and he deposits another dollars.

He has dollars in his account.

By the end of year 4, it has grown to dollars

. . and he deposits another dollars.

He has dollars in his account.

By the end of year 5, it has grown to dollars

. . and he deposits another dollars.

He has dollars in his account.

And this should equal his desired goal: $638,140.78.

.[1]

The geometric series has first term , common ratio , and terms.

. . Its sum is: .

Then [1] becomes: .

Therefore: .

is the amount he must invest yearly for 5 years to buy his dream house.That