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Difference between two investments...

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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.

Nov 26, 2017

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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.

Nov 26, 2017