Question

You want to invest some money today that will grow, and later be used to support semi-annual annuity payments of $2500.00, the first one starting exactly 6 years from today. A total of 16 payments will be received over 8 years. If interest is earned at 6% compounded quarterly, how money should be invested today?

Answer 1

Semi-annual compounding APR is:

Particulars	Amount
Given APR	6.00%
Given compounding frequency per year	4
Effective annual rate	6.136355%
(1+ 0.06/4)^4 -1
Required compounding frequency per year	2
Req period effective rate	3.0225%
(1+ 0.06136355)^1/2 -1
Required APR	6.04500%
0.030225*2

Particulars	Amount
Annuity payment	2,500.00
× PVAFD for 16 payments	12.91853
Value in 6 years	32,296.33
× PVF for six years	0.69954
Deposit today	22,592.70

Answer is:

22,592.70

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