Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years, and so on indefinitely. The interest rate to be used is 2%, compounded continuously.
The amount given by Alice to Bob at the beginning of year n is given by (n+1)*1000.
As interest is compounded continuously and the amount is received at the beginning of the year, the present value of an amount received after n years is A =...
Alice promises to pay Bob $1000 today, $2000 in one year, $3000 in two years, and so on indefinitely. The interest rate to be used is 2%, compounded continuously.
The amount given by Alice to Bob at the beginning of year n is given by (n+1)*1000.
As interest is compounded continuously and the amount is received at the beginning of the year, the present value of an amount received after n years is A = (n+1)*1000/e^(0.02*n)
The total present value of Alice's promise is
`1000+ sum_(n=1)^(oo)(n+1)*1000/e^(0.02*n) `
= 2.54942*10^6
Alice would make the largest payment to Bob approximately at the start of year 49.
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