Having trouble getting my head around this one, don't really understand what "compounded continuously" means:
Find the value at the end of 20 years of an investment of $100 which earns interest at the rate of 5% compounded continuously
2007-12-06 21:28:34 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
dP/dt = 0.05P
dP/P = 0.05t
P/P0 = e^0.05t
P = 100e^(0.05*20)
P = 100e
P ≈ $271.83
2007-12-06 22:05:29 · answer #1 · answered by Helmut 7 · 1⤊ 1⤋
Interest Rate Differential Formula
2016-12-16 11:00:04 · answer #2 · answered by ? 4 · 0⤊ 0⤋
"Compounded Continuously" or Compound Interest means that you will earn interest on interest. This means at the end of year one you will have earned 5% of £100 which now totals to £105. The second year you will earn 5% of £105 so you will now have £110.25, this carries for 20 years so you will have a total of £265.33
An equation for this is A=P(1+R)*T
Where A = final amount
P is investment
R is Interest
T is time period
2007-12-06 21:33:52 · answer #3 · answered by Anonymous · 1⤊ 3⤋
I'm actually doing this in maths at the moment...
the formula is:
A=P(I+R)*T
Key:
A=Final amount
P=Principal amount (money invested)
R=Rate of interest (written as a decimal)
*=Using the calculator 'to the power of' e.g 2*2=4 (2 times 2)
Solution:
100(1+0.05)*20
(using your calculator and typing the exact solution in it above...)
Answer:
265.33 (to 2 decimal places)
(full answer was: 265.3297705)
Hope this helped!
2007-12-06 21:36:46 · answer #4 · answered by Anonymous · 0⤊ 2⤋
approx. = 13.863yrs If you need the formula let me know
2016-05-21 23:41:43 · answer #5 · answered by ? 3 · 0⤊ 0⤋
a=pe^rt
a=100*e^(20*0.05)=$271.83
2007-12-06 21:34:35 · answer #6 · answered by someone else 7 · 2⤊ 1⤋