Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. David invested $220 in a savings account that offers a 3% return on the investment. The value of David's investment will be at least $400 after a period of years. Hint: Use the formula A = P(1 + r)t, where A is the amount after t years, P is the amount invested, r is the rate of interest, and t is the time period. Use a calculator to compute the answer, and round it off to the nearest year.

Answer 1

Answer:

The answer is 23 years.

Step-by-step explanation:

We will use the formula :

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

Here P = 220

r = 3%

A = 400

Putting these values in the formula we get,

$400=200(1+0.03)^{t}$

$2=1.03^{t}$

Taking log on both sides,

ln(1.03)t=ln 2

$t=\frac{ln(2)}{ln(1.03)}$

t=23.44 or rounding to nearest, t=23 years

The graph of the function can be shown as below.

Answer 2

Answer:

21 years.

Explanation :

Since, the amount in a saving account after t years is,

$A=P(1+r)^t$

Where, r is the annual rate ( in decimals ),

P is the invested amount,

t is the time ( in years ),

Here, P = $ 220,

r = 3 % = $\frac{3}{100}$ = 0.03,

Hence, the amount after t years in the given account,

$A=220(1+0.03)^t$

$=220(1.03)^t$

According to the question,

A ≥ $ 400,

$\implies 220(1.03)^t\geq 400$

$\implies (1.03)^t\geq \frac{400}{220}$

Taking log both sides,

$t log(1.03)\geq log(\frac{400}{220})$

$\implies t \geq \frac{log(\frac{400}{220})}{log(1.03)}$

By using calculator,

$t\geq 20.2253459349$

Hence, David's investment will be at least $400 after approximate 21 years.