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A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 4% compounded quarterly, how long will it take for the money to grow to $55,000? (Round your answer to the nearest whole number.)

Respuesta :

Answer:

8 years

Step-by-step explanation:

Compound interest formula

[tex]A(t)= A_0(1+\frac{r}{n})^{nt}[/tex]

A(t) is the final amount 55000

A_0= 40000, r= 4% = 0.04, for quarterly n=4

[tex]55000=40000(1+\frac{0.04}{4})^{4t}[/tex]

divide both sides by 40000

[tex]1375=(1+\frac{0.04}{4})^{4t}[/tex]

[tex]1375=(1.01)^{4t}[/tex]

Take ln on both sides

[tex]ln(1375)=4tln(1.01)[/tex]

divide both sides by ln(1.01)

[tex]\frac{ln 1375}{ln 1.01}=4t[/tex]

Divide both sides by 4

t=8.00108

So it takes 8 years

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