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Jlenok [28]
3 years ago
8

PLEASE HELP

Mathematics
1 answer:
Usimov [2.4K]3 years ago
5 0

Answer:

r\approx0.03\text{ or about $3\%$}

Step-by-step explanation:

The standard compound interest formula is given by:

\displaystyle A=P(1+\frac{r}{n})^{nt}

Where A is the amount afterwards, P is the principal, r is the rate, n is the times compounded per year, and t is the number of years.

Since we are compounding annually, n=1. Therefore:

\displaystyle  A = P (1+r)^{t}

Lester wants to invest $10,000. So, P=10,000.

He wants to earn $1000 interest. Therefore, our final amount should be 11000. So, A=11000.

And our timeframe is 3.3 years. So, t=3.3. Substituting these values, we get:

11000=10000(1+r)^{3.3}

Let’s solve for our rate r.

Divide both sides by 10000:

1.1=(1+r)^{3.3}

We can raise both sides to 1/3.3. So:

\displaystyle (1.1)^\frac{1}{3.3}=((1+r)^{3.3})^\frac{1}{3.3}

The right side will cancel:

\displaystyle r+1=(1.1)^\frac{1}{3.3}

So:

\displaystyle r=(1.1)^\frac{1}{3.3}-1

Use a calculator:

r\approx0.03

So, the annual rate of interest needs to be about 0.03 or 3% in order for Lester to earn his interest.

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