formula pv of annuity
Can Someone Please Help? Ordinary Annuities. FV=A ((1+i)^n-1)/i? PV=A [1-1/(1+i)^(m*n) ]/i ?
Sam Jones plans to retire at age 65. He wants to supplement his retirement by buying an annuity that will provide $2,400 each year for 10 years. If money is worth 8% compounded annually, how much will Jones have to pay for the annuity at age 65?
I think it uses one of these 3 formulas?
FV=A ((1+i)^n-1)/i
or
PV=A [1-1/(1+i)^(m*n) ]/i
or
A=(PV*i)/(1-1/(1+i)^n )
Can anyone figure this out?
PV = $16,104.20, which is how much he would have to pay for the annuity.
you should use the second formula you have, assuming this is an annuity-immediate (meaning that he pays for it at age 65 and gets the first payment at age 66)
you want the present value at age 65, and that’s PV in your equations.
PV = 2400 * (1 – ((1/(1+i))^10) / i where i = 8%
the FV formula would give you how much money he would have at the end of 10 years if he invested $2400 every year. your formula for A would allow you to solve for what the payments would need to be if you knew the present value of the annuity.
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EDIT:
Jacob S is incorrect. Sam will receive $2400 every year for 10 years, so the future payments will have a present value of less than $2400 (they will get discounted back to today). The sum of the present value of those payments will therefore be less than $24,000. Paying over $34,000 makes no sense. If that were the correct formula/price, Sam would be paying $34,000 now to get paid only $24,000 over the next 10 years. That makes no sense.
Finance Basics 5 – Learn Present Value and what it Means & Does
