Investment: collectable toys
Current yield 5% per month
Rick: Extreamly high
Your inital value is 1000 dollars
what is the doubling time, time to reach 1800, and value after 10 years?
This is compounded countinuously
5% per month compounded continuously means
A = Pe^(.05m)
To double, you need
e^(.05m) = 2
.05m = ln2
m = ln2/.05 = 13.8 months
so, slightly less than that to reach 1800 = 1000 * 1.8
In 10 years (120 months), 1000e^(.05*120) = 1000e^6 = 1000*403.4287935
To calculate the doubling time in this investment, we need to use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^n
Where:
Future Value = Present Value * 2 (since we want to double the initial value)
Interest Rate = 5% per month (which can be written as 0.05)
n = the number of months it takes to double the money
Now, let's calculate the doubling time:
2 * 1000 = 1000 * (1 + 0.05)^n
Divide both sides by 1000:
2 = (1.05)^n
To solve for n, we need to take the logarithm of both sides of the equation (using the same base):
log base 1.05 of 2 = n
Using a calculator, the answer is approximately 13.86 months. So, it would take about 13.86 months to double your initial investment.
Next, let's calculate the time it takes to reach $1800:
1800 = 1000 * (1 + 0.05)^n
Divide both sides by 1000:
1.8 = (1.05)^n
Taking the logarithm of both sides:
log base 1.05 of 1.8 = n
Using a calculator, the answer is approximately 10.83 months. So, it would take about 10.83 months to reach $1800.
Lastly, let's calculate the value after 10 years:
To do this, we can use the compound interest formula directly:
Future Value = Present Value * (1 + Interest Rate)^n
Future Value = 1000 * (1 + 0.05)^(10*12)
Future Value = 1000 * (1.05)^120
Using a calculator, the answer is approximately $4,439.24. So, the value after 10 years would be about $4,439.24.