Question

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

Answer 1

Answer:

70years

Explanation:

The future value formula for compound interest, after n interest period is

$F=P(1+i)^n$

where i is the interest rate per period in decimal form and P is the principal or present value.

The Rodriquez family is determined to purchase a $250,000 home so

F=$ 250,000

The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent.

This implies that:

$i = \frac{0.0665}{4} = 0.0016625$

For t years, the number of compounding periods will be;

$n = 4t$

We fixed the values into the formula and solve for t.

$250000=2500(1+0.0066125)^ {4t}$

$\frac{250000}{2500} =(1.0066125)^ {4t}$

$100=(1.0066125)^ {4t}$

$100=(1.0682)^ {t}$

$t = log_{1.0682}(100)$

$t = 69.8$

It will take approximately 70years