A bank account earns 3 percent interest compounded continuously. What annual amount of money must parents?

Question

each year in order to save 122000 in 14 years for a child's college expenses? Assume the annual amount is added continuously over the period of each year.

Answer 1

Your question is unclear. You say to assume the annual amount is added continuously over the year . This does not make sense.

Are you saying that the parents are depositing x$ into a bank account each year starting at year zero and that this is receiving 3% interest compounded continuosly for a year. Then the parents are depositing anther x$ at the beginning of the 2nd year and the continuous compounding continues and this goes on until the beginning of year 14 at which time the parents deposit the final x$ so that at the end of year 14 there will be 122,000 available?

If so, let me know and I will solve it for you.

Answer 2

DDY. Look at your last sentence. You are saying that a daily deposit of some seven plus bucks would be added each day to this account? Your question in the prior sentence asks for the annual amount to be added, but calls for continuous interest. You have baffled some of us, but not apparently the above answerer. I am curious about which you want though, a daily deposit or an annual deposit. They call for different equations.

Answer 3

edited
i dont learn maths anymore now. so i've forgotten the formula somehow.

122000 <= x[sum of GP,a=r=1.03,n=14]
122000 <= x[1.03^15-1.03]/(1.03-1)
122000 <= 1.03x(1.03^14 -1)/0.03
x >= 122000*3/103(1.03^14 -1)
x >= 6932.246

answer=$6932.246 annually, for 14 years.

parents have to put aside $577.69 monthly, or $19.26 per day.

Answer 4

Let:
the fractional continuous annual interest rate be r per year,
the contribution rate be p per year paid in continuously,
s be the sum accumulated after t years.

ds/dt = p + rs
int (0 to t) ds / (p + rs) = int(0 to t) dt
(1/r)( ln(p + rs) )[0 to s] = t
ln((p + rs) / p) = rt
ln(1 + rs/p) = rt
1 + rs/p = e^(rt)

rs/p = e^(rt) - 1
p = rs / (e^(rt) - 1)
= 0.03 * 122000 / (e^(0.03 * 14) - 1)
= 7012.01 per year.