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dsp73
3 years ago
13

Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the n

earest tenth of a percent, what is the rate of interest on the account?
Mathematics
1 answer:
-Dominant- [34]3 years ago
5 0

Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

A=P(1+r)^t

Plugging values in formula, we get

329.49=300(1+r)^2

\mathrm{Divide\:both\:sides\:by\:}300

\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}

\left(1+r\right)^2=1.0983

Taking square root on both sides, we get

1+r=\sqrt{1.0983}

\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}

1+r-1=\sqrt{1.0983}-1

r=\sqrt{1.0983}-1

r=1.048-1

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r  = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

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