Posted by Andrea on Wednesday, December 12, 2012 at 10:50am.
In an episode from the TV show Futurama, Phillip J. Fry had $0.93 in his bank account in 2000. In the year 3000 it had grown to $4.3 billion! What was the percent interest rate (to three decimal places) if it had been continuously compounded? What was the percent interest rate (to three decimal places) if it had been compounded quarterly?
- algebra - MathMate, Wednesday, December 12, 2012 at 11:27am
Formula for continuous interest:
take log on both sides and solve for r:
You should get around 2.2%, ASSUMING banks do not round interest deposits to the nearest cent.
If they deposit interest every two months and round the interest to the nearest cent, the money will not grow at all because interest for every 2 months is less than half a cent.
If it had been compounded quarterly, then the formula is
Again, take log on both sides,
r = (10^[log10(A/P)/(4t)]-1)*4
where log10=log to the base 10
You should get also about 2.2%, but a little less than continuous interest.
Again, it depends on how banks "round" down or round up the cent, and hope they don't have monthly charges! :)
- algebra - Reiny, Wednesday, December 12, 2012 at 11:33am
4300000= .93 e^1000r
4623655.91 = e^1000r
1000r = ln 4623655.91
r = .0153467
let the quarterly rate be i
.93(1+i)^4000 = 4300000
(1+i)^4000 = 4623655.91
i+i = 1.003844...
i = ..003844..
so the annual rate compounded quarterly is .. 0.015376 or 1.5376 %
.93 e^(.01535(1000)) = 4, 314,230 using the rounded continuous rate
.93(1+.003844)^4000 = 4,299,999.76 not bad!
- algebra - MathMate, Wednesday, December 12, 2012 at 10:48pm
Andrea, which continent are you on?
In USA, 1 billion = 10^9, and I think in UK and France, 1 billion = 10^12. This makes a big difference.
Answer This Question
More Related Questions
- algebra - Hassan deposited $7,500 into a bank account. At the end of 3 years, ...
- Pre-Algebra help PLZ!! - Hassan deposited $7,500 into a bank account. At the end...
- Calculus - Money is deposited in an account for which the interest is compounded...
- pre algebra - At the beginning of the year 2000, Bob put $100 in a savings ...
- algebra - You deposit $3000 in an account earning 7% interest compounded ...
- maths - juan had $3000 in his savings account. a year later, he had $4000 ...
- Finance - A bank offers your firm a revolving credit arrangement for up to $85 ...
- Finance - If you put $10,000 at the end of each year into a savings account that...
- math - If 3000 dollars is invested in a bank account at an interest rate of 9 ...
- Mathematics of INVESTMENT - Q: Ms. Parker deposits $8000 in one simple interest ...