PLEASE HELP!!!!
A bank account earns 9 percent interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save 250000 dollars in 9 years for a child's college expenses?

Question

PLEASE HELP!!!!
A bank account earns 9 percent interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save 250000 dollars in 9 years for a child's college expenses?

tkhunny · Answer

You can experiment and gain confidence in your result.

i = 0.09
m = Compounding periods per year
n = 9 (Total number of years)
n*m = Total number of payments
j = i/m
r = 1+j

Formulation

$Pmt\cdot (r + r^{2} + r^{3} + ... + r^{n*m}) = 250000$

$Pmt\cdot\dfrac{r-r^{n*m+1}}{1-r} = 250000$

Annual
m = 1
n*m = 9
g = 0.09
r = 1.09

Pmt = 17614.40414

Semi-Annual
m = 2
n*m = 18
g = 0.045
r = 1.045

Pmt = 8908.34869

Quarterly
m = 4
Pmt = 4480.49269

Monthly
m = 12
Pmt = 1499.48106

Weekly
m = 52
Pmt = 346.57201

Daily
m = 365
Pmt = 49.39445

Hourly
m = 365*24
Pmt = 2.05823

Minutely
m = 365*24*60
Pmt = 0.0343039853

Find the continuous formulation and see where it leads.