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Dominik [7]
3 years ago
6

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 w

ill it take for the money to grow to $55,000? (Round your answer to the nearest whole number.)
Mathematics
1 answer:
slava [35]3 years ago
8 0

Answer:

8 years

Step-by-step explanation:

Compound interest formula

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

A(t) is the final amount 55000

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

55000=40000(1+\frac{0.04}{4})^{4t}

divide both sides by 40000

1375=(1+\frac{0.04}{4})^{4t}

1375=(1.01)^{4t}

Take ln on both sides

ln(1375)=4tln(1.01)

divide both sides by ln(1.01)

\frac{ln 1375}{ln 1.01}=4t

Divide both sides by 4

t=8.00108

So it takes 8 years

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Hope you understand this, feel free to ask me anything!

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