The difference between the FV of an annuity DUE and the FV of a lump sum of $100,000 over a period of 35 years @ 6% compounded monthly is $75,000, what are the monthly annuity payments over that same period? Please explain the answer in steps, if possible. I thank you.
1)
To find out the FV of $100,000, you would use the common formula:
FV = PV x [1 + R]^N
FV =100,000 x [1 + 0.06/12]^(35*12)
FV =100,000 x [1.005]^420
FV =100,000 x 8.1235514938....
FV =$812,355.15 - This is the FV of $100,000 @6% comp.monthly.
2)
Since the annuity due is $75,000 greater than this amount, it, therefore, follows that it must be:
=$812,355.15 + $75,000=$887,355.15 - This is the FV of your annuity due.
To find the monthly payments that grew to this amount over 35 years @ 6% comp. monthly, you have to use this formula:
FV = PMT x {[1 + R]^N - 1 / R x [1+R]}, Remember this is annuity DUE, which means that the payments are made at the beginning of each month.
887,355.15 = PMT x {[1 + 0.06/12]^(35*12) - 1 / (0.06/12) x 1.005}
887,355.15 =PMT x {[[1.005]^420 -1 /0.005] x 1.005}
887,355.15 =PMT x 1,431.833850254....
PMT =887,355.15 / 1,431.833850254....
PMT =$619.73 - This is the monthly payment for the annuity due.
