Question

sofia and manuel are purchasing a home. they wish to save money for 15 years and purchase a house that has a value of $180,000 with cash. if they deposit money into an account paying 5% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?

Answer 1

We will have the following:

We will have that the value at the end will be $180 000.

The number of periods will be 15*12 = 180.

The interest per month is 0.05/12 = 0.0042

Now:

`A=(P((1+i)^n-1))/(i)_{}`

Here "A" is the value at the end, "P" will be the monthly payments, "i" the monthly interest rate and "n" the number of periods. So:

`180000=(P((1+0.0042)^(180)-1))/(0.0042)\Rightarrow P=(180000\cdot0.0042)/(((1+0.0042)^(180)-1))`

`\Rightarrow P=671.1819761\ldots\Rightarrow P\approx671.2`

So, they will need to deposit approximately $671.2 each month.