Manny and Irene will be retiring in fifteen years and would like to buy a Mexican villa. The villa costs $500,000 today, and housing prices in Mexico are expected to increase by 6% per year. Manny and Irene want to make fifteen equal annual payments into an account, starting today, so there will be enough money to purchase the villa in fifteen years. If the account earns 10% per year, what is the amount of each deposit?

Annual deposit = $37,714.37

Explanation:

Giving the following information:

The villa costs $500,000 today, and housing prices in Mexico are expected to increase by 6% per year. Manny and Irene want to make fifteen equal annual payments into an account, starting today, so there will be enough money to purchase the villa in fifteen years.

The account earns 10% per year.

First, we need to calculate the final value of the house with the following formula.

FV = PV * (1+i) ^n

FV = 500,000 * (1.06^15) = $1,198,279.1

Now, we can calculate the annual payments required:

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

A = (1,198,279.1*0.10) / [ (1.10^15) - 1]

A = $37,714.37