How long will it take for a sum of money to double itself at 10% simple interest?
P = Po + Po*r*t = 2Po.
Po + Po*0.1*t = 2Po
Divide by Po:
1 + 0.1t = 2.
0.1t = 1.
t = 10 Years.
To determine how long it will take for a sum of money to double itself at 10% simple interest, we need to use the concept of the compound interest formula.
The formula to calculate compound interest is:
A = P(1 + (r/n))^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For this particular problem, we are given that it has simple interest, not compound interest. Simple interest is calculated using the formula:
A = P(1 + rt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
t = the number of years
In this case, we want the final amount (A) to be double the principal amount (P). So, we can set up the equation as follows:
2P = P(1 + rt)
Now we can solve for t (the number of years):
2 = 1 + rt
Rearranging the equation, we get:
rt = 2 - 1
rt = 1
Now we can plug in the given interest rate (r = 0.10) to solve for t:
0.10t = 1
To isolate t, we divide both sides by 0.10:
t = 1 / 0.10
t = 10
Therefore, it will take 10 years for the sum of money to double itself at a 10% simple interest rate.