You are looking for an account to invest your $9,000 in. You want to know how many years it will take to double if the account you are putting it into gets 10% APR. Using the Rule of 70, how many years should you be expecting to leave it sit?
7 years
10 years
18 years
You take $9,000 and place it into an account that compounds quarterly (4 times a year) at 7% for 10 years. What is the account going to be worth at the end of that time? Round to the nearest penny.
$16,201.83
$15,300.00
$18,014.38
I thought it was the rule of 72.
Anyway by the "rule of 70" it would clearly take 7 years.
You multiply the time by the rate
actual time:
2 = 1.1^n
log2 = nlog 1.1
n = log2/log1.1 = 7.27
the rule of 72 would have given an answer of 72/10 = 7.2 , a bit closer to the real answer.
#2, amount = 9000(1.0175)^40 = .....
I see the correct answer in your list
To answer the first question, we can use the Rule of 70 to estimate the number of years it would take for your investment to double. The Rule of 70 allows us to approximate the time it takes for an investment to double by dividing 70 by the annual percentage rate (APR).
In this case, the APR is 10%, so we can calculate the number of years using the formula:
Number of years ≈ 70 / APR
Substituting the value of 10% into the formula, we get:
Number of years ≈ 70 / 10%
≈ 70 / 0.10
≈ 700 / 10
≈ 70
Therefore, according to the Rule of 70, it would take approximately 70 years for your investment to double.
For the second question, to calculate the value of the investment after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = The future value of the investment
P = The initial investment amount ($9,000 in this case)
r = The annual interest rate divided by 100 (0.07 in this case, as it is 7%)
n = The number of times interest is compounded per year (4 in this case, as it compounds quarterly)
t = The number of years (10 in this case)
Plugging in the values into the formula, we get:
A = 9,000(1 + 0.07/4)^(4*10)
≈ 9,000(1 + 0.0175)^40
≈ 9,000(1.0175)^40
Calculating this expression, we find that the value of the investment after 10 years is approximately $16,201.83.
Therefore, the correct answer is "$16,201.83".