This is thrown randomly into a take home math quiz I have and I have never seen one in my life. Any help would be appreciated.
Sean invests $10,000 at an annual rate of 5% compounded continuously, according to the formula A=Pe^rt, where A is the amount, P is the Principal, e=2.718, r is the rate of interest, and t is time, in years.
Determine to the nearest dollar, the amount of money he will have after 2 years.
Determine how many years, to the nearest year, it will take for his initial investment to double.
2007-04-26 13:28:57 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
well, you have to use a calculator to answer these two questions. There is an e^x button on most scientific calculators. If not, use the approximation of e your teacher has provided as the base of the exponent.
(1) A = 10000e^(.05*2)
A = 10000e^(.1)
A = 11,052
(2) There is a really easy formula to compute doubling time of an investment that is compounded continuously. Doubling time = ln 2 / rate
Therefore, doubling time = ln 2 / .05 = 13.9 years or 14 years to nearest year.
2007-04-26 13:45:49 · answer #1 · answered by Kathleen K 7 · 0⤊ 0⤋
For the first one:
A = Pe^rt
A = 10000e^(.05*2) = 10000*e^ .1
Use a calculator or e = 2.718281828(approx)
to get A = 11051.70
Second one:
20000 = 10000e^ .05t
2 = e^.05t
.05t = ln 2
t = ln2/.05.
With the aid of a calculator, we find t = 13.86 years(approx).
2007-04-26 21:06:21 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
Investment to Double
-----------------------------
2P = P e ^ rt
2 = e ^ rt
ln2 = rt
t = ln2 / r = .69 / .05 = 13.86 years
Amount of Money after 2 years
A = 10000 * e ^ (.05 * 2)
2007-04-26 20:43:22 · answer #3 · answered by Danielle B 1 · 0⤊ 0⤋