Question 1204592: An amount of money is invested at 12%/a interest. Write an equation and solve it to determine the length of time it will take for each of the following events to occur. Round answers to the nearest tenth of a year.
- the original amount to double if interest is compounded annually
- the original amount to triple if interest is compounded monthly
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! An amount of money is invested at 12%/a interest. Write an equation and solve it to determine the length of time it will take for each of the following events to occur. Round answers to the nearest tenth of a year.
- the original amount to double if interest is compounded annually\\
A/P=2
A/P= (1+r)^n
2= 1.12^n
log 2= n log 1.12
log2/log1.12= n
n= 6.116 years (approx)
- the original amount to triple if interest is compounded monthly
A/P=3
r=12% = 0.12
compounded monthly =0.01
A/P = 1.01^12t
3= 1.01^12t
log3= 12t log 1.01
log 3/12*log 1.01 =t
t= 9.2 years
Answer by ikleyn(52907)  (Show Source):
You can put this solution on YOUR website! .
An amount of money is invested at 12%/a interest. Write an equation and solve it to determine the length of time
it will take for each of the following events to occur. Round answers to the nearest tenth of a year.
- (a) the original amount to double if interest is compounded annually
- (b) the original amount to triple if interest is compounded monthly
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The instruction in the post " Round answers to the nearest tenth of a year " is incorrect.
The answer should be given in integer number of compound periods:
- in part (a), the answer should be given in years (concretely,
from the solution of the other tutor, the answer 6.116 years should be rounded to 7 years,
when the bank will complete 7-th compounding);
- in part (b), the answer should be given in months (concretely,
from the solution of the other tutor, the answer 9.2 years should be rounded to 9 years and 3 months,
when the bank will complete the last compounding).
In such problems, the amount at the account is not a continuous function.
It is a discrete function, which changes its values only at the end of each compound period.
The event (a) will not occur at 6.116 years. It will occur at 7 years, and not earlier.
The event (b) will not occur at 9.2 years. It will occur at 9 years and 3 months, and not earlier.
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To see many other similar (and different) solved problems, look into the lesson
- Problems on discretely compound accounts
in this site, and learn the subject from there.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.
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