Question

Based on the rule of 72 (your text page 21), how many years will it take for a $1,000 investment to grow to $2,000, assuming the investment grows at 6% per year?

Answer 1

Answer:it will take 12 years

Explanation:

Initial amount invested into the account is $1000 This means that the principal,

P = 1000

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 6%. So

r = 6/100 = 0.06

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. The total amount is given as $2000

Therefore

2000 = 1000 (1+0.06/1)^1×t

2000 = 1000(1.06)^t

2000/1000 = (1.06)^t

2 = (1.06)^t

t = 12

Answer 2

12 years.

Explanation:

We are asked to find the time it will take to an amount of $1000 to grow to $2000 at a rate of 6% per year.

To find the number of years it will take the amount to double, we will divide 72 by growth rate that is 6% is this case.

`\text{Time it will take to double the amount}=(72)/(6)`

`\text{Time it will take to double the amount}=12`

Therefore, it will take 12 years for a $1,000 investment to grow to $2,000, assuming the investment grows at 6% per year.