Asked by Jus
An investment pays 8% interest, compounded annually.
a) write an equation that expresses the amount, A, of the investment as a function of time, t, in years.
b) determine how long it will take for this investment to double in value and then to triple in value.
c) determine the percent increase in value of the account after 5 years and then after 10 years.
d) explain why the answers to parts b and c do not depend on the amount of the initial principal.
Can someone explain to me how to get started? I do not know where to start except for the fact that I need to make an exponential function.
a) write an equation that expresses the amount, A, of the investment as a function of time, t, in years.
b) determine how long it will take for this investment to double in value and then to triple in value.
c) determine the percent increase in value of the account after 5 years and then after 10 years.
d) explain why the answers to parts b and c do not depend on the amount of the initial principal.
Can someone explain to me how to get started? I do not know where to start except for the fact that I need to make an exponential function.
Answers
Answered by
Damon
after one year
A = Ao (1.08)
after two years
A = Ao (1.08)(1.08)
after three years
A = Ao (1.08)(1.08)(1.08)
after t years
A = Ao (1.08)^t
When is A/Ao = 2?
2 = 1.08^t
log 2 = t log 1.08
.301 = t * .0334
t = 9.01 years to double
That should get you started.
A = Ao (1.08)
after two years
A = Ao (1.08)(1.08)
after three years
A = Ao (1.08)(1.08)(1.08)
after t years
A = Ao (1.08)^t
When is A/Ao = 2?
2 = 1.08^t
log 2 = t log 1.08
.301 = t * .0334
t = 9.01 years to double
That should get you started.
Answered by
Jus
did i do part c right?
c) determine the percent increase in value of the account after:
5 years,
A=(1.08)^5
=1.47
therefore 1.47 % increase???
c) determine the percent increase in value of the account after:
5 years,
A=(1.08)^5
=1.47
therefore 1.47 % increase???
Answered by
Jus
c) continued:
after 10 years
A=(1.08)^10
=2.16
therefore 2.16% increase?
Am I doing this right?
d) Explain why the answers to parts b and c do not depend on the amount of the initial principal.
after 10 years
A=(1.08)^10
=2.16
therefore 2.16% increase?
Am I doing this right?
d) Explain why the answers to parts b and c do not depend on the amount of the initial principal.
Answered by
Damon
" =1.47
therefore 1.47 % increase??? "
A factor of 1.47 is a 47% increase
100 * final/original = 147/1 =147 %
which is 47 % over the original 100%
therefore 1.47 % increase??? "
A factor of 1.47 is a 47% increase
100 * final/original = 147/1 =147 %
which is 47 % over the original 100%
Answered by
Damon
2.16 * 100 = 216 % of original
216 % - original 100% = 116% increase
216 % - original 100% = 116% increase
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.