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NeTakaya
3 years ago
15

Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds cont

inuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

\approx 17.5% per annum

Step-by-step explanation:

<u>Given:</u>

Money invested = $20,000 at the age of 20 years.

Money expected to be $500,000 at the age of 40.

Time = 40 - 20 = 20 years

<em>Interest is compounded annually.</em>

<u>To find:</u>

Rate of growth = ?

<u>Solution:</u>

First of all, let us have a look at the formula for compound interest.

A = P \times (1+\frac{R}{100})^T

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.

Here, We are given:

P = $20,000

A = $500,000

T = 20 years

R = ?

Putting all the values in the formula:

500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%

So, the correct answer is \approx <em>17.5% </em>per annum and compounding annually.

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