- #1
wakko101
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I'm trying to figure out the solution to a differential equation that describes the accrued interest on an annuity - rather than a lump sum at the beginning, we're dealing with multiple and regular deposits. The prof implied that we would have to solve for the dif eq'n
S' = k + rS
where k is the deposit, r the interest rate and S(t) the amount of money accrued at time t. I think I've solved for this particular equation (with intinial condition S(0) - So) which is
S(t) = (So + k)e^rt - k
but I have two questions. First, this doesn't seem right in terms of the fact that I'm subtracting k at the end there. And secondly, should k somehow be in terms of t as well (i.e. k(t) since the deposits are regular, i.e. at time t, I will have made k(t) deposits?)
Any insight would be appreicated...
Thanks,
W.
S' = k + rS
where k is the deposit, r the interest rate and S(t) the amount of money accrued at time t. I think I've solved for this particular equation (with intinial condition S(0) - So) which is
S(t) = (So + k)e^rt - k
but I have two questions. First, this doesn't seem right in terms of the fact that I'm subtracting k at the end there. And secondly, should k somehow be in terms of t as well (i.e. k(t) since the deposits are regular, i.e. at time t, I will have made k(t) deposits?)
Any insight would be appreicated...
Thanks,
W.