You have 4 different investment options
4% interest
7% compound continuously
19% annually
5% every month
You have 1000 dollars
how long does it take for the value to double in each other investment options?
How long does it take until 1000 becomes 1800?
What does the 1000 dollars become after 10 years with each investment plan?
The amount you start with does not matter, as long as it doubles
e.g. 10000 ---> 2000
1 ----> 2
I will do the 19% case, you do the others
1(1.19)^t = 2
1.19^t = 2
take log of both sides and use log rules
t log 1.19 = log 2
t = log2/log1.19 = appr 3.985 years
7% compound continuously ----- takes special care
1e^(.07t) = 2
now take ln of both sides, remember lne = 1
.07t lne = ln2
.07t = ln2
t = ln2/.07 = appr 9.9
let me know what you get for the others.
To find out how long it takes for the value to double in each investment option, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of compounding periods per year
t is the number of years
Let's calculate the time it takes for the value to double in each investment option:
1. 4% interest:
To double the initial investment, we need to find when A becomes 2000:
2000 = 1000 * (1 + 0.04)^t
Divide both sides by 1000:
2 = (1.04)^t
To solve for t, we can take the natural logarithm of both sides:
ln(2) = t * ln(1.04)
Now we divide ln(2) by ln(1.04) to find t.
2. 7% compound continuously:
To double the initial investment, we can use the formula:
2000 = 1000 * e^(0.07t)
Divide both sides by 1000:
2 = e^(0.07t)
To solve for t, we can take the natural logarithm of both sides:
ln(2) = 0.07t
Now divide ln(2) by 0.07 to find t.
3. 19% annually:
To double the initial investment, we need to find when A becomes 2000:
2000 = 1000 * (1 + 0.19)^t
Divide both sides by 1000:
2 = (1.19)^t
To solve for t, take the logarithm of both sides:
log(2) = t * log(1.19)
Now divide log(2) by log(1.19) to find t.
4. 5% every month:
To double the initial investment, we need to find when A becomes 2000:
2000 = 1000 * (1 + 0.05/12)^(12t)
Divide both sides by 1000:
2 = (1.0041667)^^(12t)
To solve for t, take the logarithm of both sides:
log(2) = 12t * log(1.0041667)
Now divide log(2) by 12 * log(1.0041667) to find t.
To determine how long it takes until $1000 becomes $1800, we can use the same formulas and replace the final amount (A) with $1800.
To figure out what $1000 becomes after 10 years with each investment plan, we can plug in the values into the formulas and calculate the final amount (A) by setting t = 10 years and P = $1000.