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