Question

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?

Answer 1

Annual deposit= $37,714.37

Step-by-step 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