The Rodriguez family is determined to purchase a $250,000 home without incurring any debt. The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent, compounded quarterly. How long will it be until the family can purchase a home

70 years

Explanation:

Amount, A = $250,000

Principal, P=$2500

Rate, R=$6.65 compounded quarterly. This means that in every 3 months of the year, the interest the principal yielded is added to the principal to become the new principal for every 3 months.

Formular:

Amount, A = P[1 + (R/100*4) ]^4t

Where P = principal

R = rate

t = number of years

The "4" in the formular shows that the interest is compounded "quarterly".

In this problem, we are looking for the number of years (which is "t") it will take to save up to $250000.

Substituting the values:

250,000=2500[1 + (6.65/100*4) ]^4t

Dividing both sides by 2500,

We have:

100=[1 + (6.65/100*4) ]^4t

Simplifying the terms inside brackets, we have:

100=1.016625^4t

Find the value of t which when substituted in the expression will give 100. The value of t = 70.

Hence it will take 70 years to save $250000