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**Unformatted text preview: **ties: Future Value and Present Value 59 Exercise 10.4 (continued) 5. Given: PMT = $1500, i = 7.9%, n = 1(8) = 8, and PV = $6383.65
At a focal date at the end of the period of deferral,
FV of $6383.65 = PV of ordinary annuity
−8 d = $1500 1 − 1.079 $6383.65 (1.079 ) 0.079 = $8652.77 Using formula (9-2) to calculate d, $8652.77 FV ln ln PV = $6383.65 = 4.00 payment intervals
d= ln (1.079 )
ln(1 + i )
The period of deferral is 4 years. 60 Business Mathematics in Canada, 7/e Exercise 10.4 (continued)
7. Given: PMT = $400, i = 9.75% = 0.8125%, n = 12(14) = 180, and PV = $33,173.03
12
At a focal date at the end of the period of deferral,
FV of $33,173.03 = PV of ordinary annuity 1 − 1.008125 −180 d = $37,758.55
$33,173.03 (1.008125 ) = $400 0.008125 Using formula (9-2) to calculate d, $37,758.55 FV ln ln PV = $33,173.03 = 16.00 payment intervals
d= ln(1 + i )
ln (1.008125 )
The period of deferral is 16 months or 1 year and 4 months.
9. Today's economic value of the future payments is
their present value (discounted at the time value of
money). Viewing the payments as a deferred
ordinary simple annuity,
PMT = $1500, n = 4(11) = 44, d = 4(5.75) = 23,
and i = 6.5% = 1.625%
4
1 − (1 + i ) − n PV(5.75 years from now) = PMT i = $1500 1 − 1.01625 −44 0.01625 = $46,891.229
PV(today) = FV (1 + i ) − d 6.5 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4)
44 N 1500 PMT
0 FV CPT PV Ans: −46,891.229 Same I/Y, P/Y, C/Y
23 N 0 PMT
46891.229 FV CPT PV Ans: −32,365.24 = $46,891.229 (1.01625 ) −23
= $32,365.24 Chapter 10: Ordinary Annuities: Future Value and Present Value 61 Exercise 10.4 (continued)
11. Today’s economic value economic is the
present value.
For the $1000 annuity,
1 − (1 + i ) − n PV(today) = PMT i 1 − 1.065 − 10
= $1000 0.065 = $7188.83
For the $2000 annuity,
PV(10 years from now) 1 − 1.065 −10
= $2000 0.065 = $14,377.66
PV(today) = $14,377.66
1.065 10 6.5 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1)
10 N 1000 PMT
0 FV CPT PV Ans: −7188.83 Same I/Y, P/Y, C/Y
Same N, FV
2000 PMT
CPT PV Ans: −14,377.66 = Same I/Y, P/Y, C/Y, N
0 PMT
1...

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