a sum of money doubles in 20 years on simple interest. it will triple at the same rate in ?
60
2=1(1+i)^20
take the log of each side
log2=20(log(1+i)
log(1+i)=log2/20=.01505
now take the antilog
1+i=10^(.01505)=1.03526
so i=3.526 percent
triple?
3=(1.03526)^t
take the log of each side
log3=t*log(1.03526)
t= log3/log(1.03526)= .4771 /.01505
almost 32 years
Hmm, let me calculate this while juggling imaginary coins. Okay, so if the sum of money doubles in 20 years on simple interest, then we can assume an interest rate of 100% over 20 years. Now, to find out when it will triple, I'll need to double the rate.
Therefore, with my clown calculator, it looks like the sum of money will triple in... ta-da! 40 years! Just be patient, and your money will have three times the fun!
To determine the time it takes for a sum of money to triple on simple interest, we need to consider the doubling time and the relationship between doubling and tripling.
First, let's think about the doubling period. We are given that the sum of money doubles in 20 years on simple interest. This means that the interest earned in 20 years is equal to the principal amount (the initial sum of money).
Now, let's move on to finding the time it takes to triple the sum of money. Since the sum doubles in 20 years, we can conclude that in the next 20 years (from year 20 to year 40), it will double again.
So, after 40 years, we have two doublings, which means the sum has quadrupled. This implies that from year 20 to year 40, the sum has tripled because tripling is half of quadrupling.
Therefore, the sum of money will triple in 40 years on simple interest.
To summarize:
- The sum doubles in 20 years.
- The sum triples in 40 years.
2=1(1+i)^20
take the log of each side
log2=20(log(1+i)
log(1+i)=log2/20=.01505
now take the antilog
1+i=10^(.01505)=1.03526
so i=3.526 percent
triple?
3=(1.03526)^t
take the log of each side
log3=t*log(1.03526)
t= log3/log(1.03526)= .4771 /.01505
almost 32 years
check that