Answer:
70years
Explanation:
The future value formula for compound interest, after n interest period is
[tex]F=P(1+i)^n[/tex]
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:
[tex]i = \frac{0.0665}{4} = 0.0016625[/tex]
For t years, the number of compounding periods will be;
[tex]n = 4t[/tex]
We fixed the values into the formula and solve for t.
[tex]250000=2500(1+0.0066125)^ {4t}[/tex]
[tex] \frac{250000}{2500} =(1.0066125)^ {4t}[/tex]
[tex]100=(1.0066125)^ {4t}[/tex]
[tex]100=(1.0682)^ {t}[/tex]
[tex]t = log_{1.0682}(100) [/tex]
[tex]t = 69.8[/tex]
It will take approximately 70years
