Question

Using the appropriate present value table and assuming a 12% annual interest rate, determine the present value on December 31, 2018, of a five-period annual annuity of $5,600 under each of the following situations: (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) 1.The first payment is received on December 31, 2019, and interest is compounded annually. 2.The first payment is received on December 31, 2018, and interest is compounded annually. 3.The first payment is received on December 31, 2019, and interest is compounded quarterly.

Answer 1

1.The first payment is received on December 31, 2019, and interest is compounded annually.

The Present Value of ordinary annuity = Annual Payment x Present Value factor for ordinary annuity at 12%, 5 Years

= Annual Payment x [PVA of $1, 12%, 5 Years]

= $5,600 x 3.60478

= $20,187

2.The first payment is received on December 31, 2018, and interest is compounded annually.

The Present Value of an annuity due = Annual Payment x Present Value factor for an annuity due at 12%, 5 Years

= Annual Payment x [PVAD of $1, 12%, 5 Years]

= $5,600 x 4.03735

= $22,609

3.The first payment is received on December 31, 2019, and interest is compounded quarterly.

IF the compounding is done quarterly, Interest Rate would be 3% (12% / 4 Quarters) and the number of years would be 20 years (5 Years x 4 Quarter)

Present Value of annuity = $5,600/(1.03)⁴ + $5,600/(1.03)⁸ + $5,600/(1.03)¹² + $5,600/(1.03)¹⁶ + $5,600/(1.03)²⁰

= [$5,600/1.12551] + [$5,600/1.26677] + [$5,600/1.42576] + [$5,600/1.60471] + [$5,600/1.80611]

= $4,976 + $4,421 + $3,928 + $3,490 + $3,101

= $19,914