For each of the following situations involving annuitities solve for the unknown assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1). Present Value Annuity Amount i = n =
3000 8% 5
242980 75000 4
161214 20000 9%
500000 80518 8
250000 10% 4

A) $11,978.10

B) 9%

C) 15 years

D) 6%

E) $78,866.84

Explanation:

Present Value            Annuity Amount            i =              n =

       A                              3000                        8%              5

242980                         75000                         B               4

161214                            20000                        9%             C

500000                          80518                         D               8

250000                            E                           10%              4

A = $3,000 x 3.9927 = $11,978.10

B:   annuity factor = $242,980 / $75,000 = 3.23973

using the annuity table, a 9% annuity for 4 years has a factor = 3.2397

C: annuity factor = $161,214 / $20,000 = 8.0607

using the annuity table, a 9% annuity for 15 years has a factor = 8.0607

D: annuity factor = $500,000 / $80,518 = 6.20979

using the annuity table, a 6% annuity for 8 years has a factor = 6.2098

E: annuity payment = present value / annuity factor = $250,000 / 3.1699 (annuity factor 10%, 4 years) = $78,866.84