Question
What single deposit today in an account paying 7% interest compounded continuously would yield $18500 in 10yr?
Answers
Damon
r = interest percent/100
dy/dt = r y
y = a e^kt
dy/dt = ak e^kt = r a e^kt
r = k
so
y = a e^rt
note when t = 0, y = a the original deposit
18500 = a e^(.07*10)
ln (18500/a) = .7
ln 18500 - ln a = .7
9.83 - .7 = ln a
ln a = 9.1255
a = 9186.83
check y = 9187 e^(.7)
y = 18500 check
dy/dt = r y
y = a e^kt
dy/dt = ak e^kt = r a e^kt
r = k
so
y = a e^rt
note when t = 0, y = a the original deposit
18500 = a e^(.07*10)
ln (18500/a) = .7
ln 18500 - ln a = .7
9.83 - .7 = ln a
ln a = 9.1255
a = 9186.83
check y = 9187 e^(.7)
y = 18500 check