Asked by Judy

Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 5% per annum compounded monthly, how much does she need now to guarantee herself $900 every month for the next 25 years?
Answered by Reiny
Present Value
= 900(1 - 1.0041666..)^-300)/.0041666...
= $153,954.05
Answered by Judy
Reiny, 153,954.05 is coming up wrong. any suggestions?
Answered by Jonas
PV = Integral from 0 to T of R(t)e^(-rt)dt
where R(t) is dollars per year continuously for T, T is years, r is interest rate.

PV = Integral 0 to 25 of (900*12)e^(-.05t)dt
** Take anti-derivative **
= (10800/-.05)e^(-.05t) evaluated from 0 to 25

= (10800/-.05)e^(-.05(25)) - (10800/-.05)e^(-.05(0))

PV = $154114.96
Answered by Jonas
PV = Integral from 0 to T of R(t)e^(-rt)dt
where R(t) is dollars per year continuously for T, T is years, r is interest rate.

PV = Integral 0 to 25 of (900*12)e^(-.05t)dt
** Take anti-derivative **
= (10800/-.05)e^(-.05t) evaluated from 0 to 25

= (10800/-.05)e^(-.05(25)) - (10800/-.05)e^(-.05(0))

PV = $154114.96

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