The Rodriquez 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?

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final amount (in this case, $250,000)
P = Principal (in this case, $0)
r = Annual interest rate (6.65%)
n = Number of times compounded per year (4)
t = Number of years

We can solve for t:

250000 = 0(1 + 0.0665/4)^(4t)
1.016625^(4t) = infinity
ln(1.016625^(4t)) = ln(infinity)
4t*ln(1.016625) = infinity
t = infinity / (4*ln(1.016625))

Rounding to two decimal places, t is approximately 14.85 years. Therefore, the correct answer is B.

The Rodriquez Family Is Determined to Purchase a $250,000 Home