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**Unformatted text preview: **4377.66 FV CPT PV Ans: −7659.35 $7659.35
The $2000 annuity has the greater (by $470.52) economic value. 62 Business Mathematics in Canada, 7/e Exercise 10.4 (continued)
13. The price paid will be the present value of the payments discounted at the required rate of
return. Since the first payment is due in 6 months, the period of deferral is 5 months (in
order to treat the payments as a deferred
ordinary annuity).
18 I/Y P/Y 12 ENTER %
Given: PMT = $231, n = 15, d = 5, and i = 182 =
(making C/Y = P/Y = 12)
1
1.5%
15 N 231 PMT
1 − (1 + i ) − n 0 FV PV(5 months from now) = PMT i
CPT PV Ans: –3082.287 1 − 1.015 −15 = $231 0.015 = $3082.287 PV(today) = FV (1 + i ) − d = $3082.29 (1.015 ) −5
= $2861.16
The finance company will pay $2861.16 for
the contract. Same I/Y, P/Y, C/Y
5 N 0 PMT
3082.287 FV CPT PV Ans: −2861.16 15. The original loan equals the present value of the payments. Thus,
PV = $35,000 with PMT = $1573.83, n = 4(12) = 48, and i = 10% = 2.5%.
4
At a focal date at the end of the period of deferral,
FV of $35,000 = PV of ordinary annuity 1 − 1.025 −48 = $43,710.22
$35,000 (1.025 ) d = $1573.83 0.025 Using formula (9-2) to calculate d, $43,710.22 FV ln ln PV = $35,000 = 9.00
d=
ln(1 + i )
ln (1.025 )
The period of deferral was 9 quarters long. The interval between the date of the
loan and the first payment was 10 quarters or 2 years and 6 months. Exercise 10.4 (continued)
17. Given: For the initial investment, PV = $10,000, i = 8.5% = 4.25%.
2
For the deferred annuity, PMT = $1000, n = 40, and i = 4.25%.
At a focal date at the end of the period of deferral,
8.5 I/Y FV of $10,000 = PV of ordinary annuity P/Y 2 ENTER −40 d = $1000 1 − 1.0425 (making C/Y = P/Y = 2)
$10,000 (1.0425 ) 0.0425
40 N 1000 PMT
= $19,077.27
0 FV Chapter 10: Ordinary Annuities: Future Value and Present Value
CPT PV 63 Ans: –19,077.27 Using formula (9-2) to calculate d, $19,077.27 FV ln ln PV = $10,000 = 15.52
d=
ln(1 + i )
ln (1.0425 )
The period of deferral is 15.52 half years
o...

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