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Juan deposited $7000 into an account with a 3.4% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $9737?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

User Feyyaz
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1 Answer

4 votes

Answer:

It will take approximately 6.89 years for the investment to grow to $9737.

Explanation:

We can use the formula for compound interest to solve this problem:

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

Where:

A = the future value of the investment

P = the present value of the investment

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know that P = $7000, r = 0.034, n = 4 (since the interest is compounded quarterly), and we want to find t when A = $9737.

$9737 = $7000(1 + 0.034/4)^(4t)

Divide both sides by $7000:

1.391 = (1 + 0.034/4)^(4t)

Take the natural logarithm of both sides:

ln(1.391) = ln[(1 + 0.034/4)^(4t)]

Use the power rule of logarithms:

ln(1.391) = 4t * ln(1 + 0.034/4)

Divide both sides by 4 ln(1 + 0.034/4):

t = ln(1.391) / [4 * ln(1 + 0.034/4)]

Using a calculator, we find:

t ≈ 6.89 years

Therefore, it will take approximately 6.89 years for the investment to grow to $9737.

User Quinn Wilson
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