Posted by Anne on Thursday, February 9, 2012 at 1:57am.
The associated exponential model for the value of a deposit after t years is
A(t) = 7000(1 + (0.0394/12))^12t.
At the start of which year will an investment of $7,000 made at the beginning of 2007 first exceed $11,000? (Round your answer the nearest whole number.)
I don't quite understand the question, but multiplying it out I got:
If t=1 then the answer 7280
If t=2 then the answer 14561.7
I don't understand the amount of years. How do I calculate that?
- Math - Reiny, Thursday, February 9, 2012 at 8:33am
The formula finds the amount at the end of so many months
notice the exponent is 12t, so if there are 3 years, t - 3 , but the exponent is 36 (36 months in 3 years)
also notice that the interest rate of .0394 (or 3.94%) is an annual rate, so it is also divided by 12
so let's set A(t) = 11000
11000 = 7000 (1.003283333)^12t
11000/7000 = (1.00328333)^12t
1.003283333^12t = 1.571428571
now take log of both sides and use the log rules
log(1.003283333^12t) = log(1.571428571)
12t log (1.003283333) = log(1.571428571)
12t = log 1.571428.)/(log 1.0032833..) = 137.886 months
or 11.5 years
So we will reach the 11000 after 11.5 years, so according to your question it will have exceeded the 11000 mark at the beginning of year 12.
if t = 11 , A(11) = 7000(1.00328333)^132 = 10789.79 , (not there yet)
if t = 12 , A(12) =7000(1.003283333)^144 = 11222.67
btw, you calculation for t = 2 is incorrect
A(2) = 7000(1.00328333)^24 = 7572.94
Answer This Question
More Related Questions
- math - You need $28,974 at the end of 10 years, and your only investment outlet ...
- Math-Exponential functions - An investment of $5,000 is made with three options:...
- accounting - You need $28,974 at the end of 10 years, and your only investment ...
- Calculus - I am confused on how to solve this problem : $5000 is invested for 4 ...
- Math (difficult) - The value of a new car purchased for $28,000 decreases 8% per...
- exponential function - An investment pays 8% interest, compounded annually. a) ...
- precalculus - the value of a particular investment follows a pattern of ...
- Algebra word problem - please help me with the following: The value of a ...
- math- HELP! - The value of a particular investment follows a pattern of ...
- Math - The value of a particular investment follows a pattern of exponential ...