*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **t required to fund each annuity is the present value of the annuity
discounted at the interest rate the money can earn. For both annuities,
PMT = $200 monthly and i = 6% = 0.5%
12
For the 30-year annuity,
1 − ( 1 + i ) −n 1 − 1.005 − 360 = $33,358.32 = $200 PV = PMT 0.005
i For the 20-year annuity, PV = $27,916.15. It requires
$33,358.32 – $27,916.15 = $5442.17 more
to fund the extra 10 years. (This is only about 20% more money.) 52 Business Mathematics in Canada, 7/e Exercise 10.3 (continued)
19. The amount François and Pat must pay is the present value of all of the payments.
The desired payment stream is equivalent to a succession of four 5-year annuities of:
(i) $2000 per quarter for the first 5 years, (ii) $2500 per quarter for the next 5 years,
(iii) $3000 per quarter for the next 5 years, and (iv) $3500 per quarter for the final 5 years.
The present values of these annuities (at their respective beginnings) are: 1 − 1.0125− 20 (i) PV = $2000 (ii) $43,998.290 0.0125 = $35,198.632; 1 − 1.0125− 20 (iii) PV = $3000 0.0125 = $52,797.948; (i)
(ii)
5 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4)
20 N 2000 PMT
0 FV CPT PV Ans: –35,198.632 $35,198.632 +
$43,998.290
+
1.012520
$52,797.948
+
1.012540
$61,597.606
1.012560 (iv) $61,597.606
(iv) Same I/Y, P/Y, C/Y
Same N, FV
3000 PMT
CPT PV Ans: –52,797.948 Same I/Y, P/Y, C/Y
Same N, FV
2500 PMT
CPT PV Ans: –43,998.290 (iii) Same I/Y, P/Y, C/Y
Same N, FV
3500 PMT
CPT PV Ans: –61,597.606 The present value today of these four
amounts is Same I/Y, P/Y, C/Y
20 N 0 PMT
43998.290 FV CPT PV Ans: –34,319.042 Same I/Y, P/Y, C/Y
60 N 0 PMT
61597.606 FV CPT PV Ans: –29,232.228 Same I/Y, P/Y, C/Y
40 N 0 PMT
52797.948 FV CPT PV Ans: –32,122.976 = $35,198.632 + $34,319.042 + 32,122.976 + 29,232.254
= $130,872.90
François and Pat must pay $130,872.90. Exercise 10.3 (continued)
21. Original loan = Present value of all payments
%
Given: PMT = $2000, n = 10, and i = 71 = 7% Chapter 10: Ordinary Annuities: Future Value and Present Value 7 I/Y P/Y 1 ENT...

View
Full
Document