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Q6. We have invested $15000 in an account compounded quarterly.

After 6 years, the account balance is $21000. What is the annual
interest rate of this account?

User Meeh
by
7.6k points

1 Answer

3 votes

Answer:

10.4%

Step-by-step explanation:

To calculate the annual interest rate of the account, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Final account balance ($21,000 in this case)

P = Principal amount ($15,000 in this case)

r = Annual interest rate (to be determined)

n = Number of times interest is compounded per year (quarterly compounding in this case)

t = Number of years (6 years in this case)

Plugging in the given values, the equation becomes:

$21,000 = $15,000 * (1 + r/4)^(4*6)

To solve for r, we need to rearrange the equation and isolate r:

(1 + r/4)^(24) = $21,000 / $15,000

(1 + r/4)^(24) = 1.4

Now, take the 24th root of both sides to isolate (1 + r/4):

1 + r/4 = (1.4)^(1/24)

1 + r/4 = 1.026

Subtract 1 from both sides and multiply by 4:

r = (1.026 - 1) * 4

r = 0.104 or 10.4%

Therefore, the annual interest rate of this account is 10.4%.

User Andrewkittredge
by
7.8k points
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