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# Time Value of Money

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There are 3 parts to this; part of this has been completed
1. Present value calculation
2. Future value of annuity: ordinary annuity and annuity due
3. Loan interest deductions

1. Present value calculation:
A PVIF &#61501; 1 &#61624; (1 &#61483; 0.02)4 &#61501; ??
B PVIF &#61501; 1 &#61624; (1 &#61483; 0.10)2 &#61501; ??
C PVIF &#61501; 1 &#61624; (1 &#61483; 0.05)3 &#61501; ??
D PVIF &#61501; 1 &#61624; (1 &#61483; 0.13)2 &#61501; ??

2. Future value of an annuity
a. Future value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity (2) Annuity Due
FVAk%,n &#61501; PMT&#61472;&#61620;&#61472;(FVIFAk%,n) FVAdue &#61501; PMT&#61472;&#61620;&#61472;[(FVIFAk%,n&#61472;&#61620;&#61472;(1 &#61483; k)]
A FVA8%,10 &#61501; \$2,500&#61472;&#61620;&#61472;14.487 FVAdue &#61501; \$2,500&#61472;&#61620;&#61472;(14.487&#61472;&#61620;&#61472;1.08)
FVA8%,10 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: ?? Calculator solution: \$??
B FVA12%,6 &#61501; \$500&#61472;&#61620;&#61472;8.115 FVAdue &#61501; \$500 &#61620;( 8.115&#61472;&#61620;&#61472;1.12)
FVA12%,6 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
C FVA20%,5 &#61501; \$30,000&#61472;&#61620;&#61472;7.442 FVAdue &#61501; \$30,000&#61472;&#61620;&#61472;(7.442&#61472;&#61620;&#61472;1.20)
FVA20%,5 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
D FVA9%,8 &#61501; \$11,500&#61472;&#61620;&#61472;11.028 FVAdue &#61501; \$11,500&#61472;&#61620;&#61472;(11.028&#61472;&#61620;&#61472;1.09)
FVA9%,8 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$138,241.92
E FVA14%,30 &#61501; \$6,000&#61472;&#61620;&#61472;356.787 FVAdue &#61501; \$6,000&#61472;&#61620;&#61472;(356.787&#61472;&#61620;&#61472;1.14)
FVA14%,30 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
b. The annuity due results in a ???? future value in each case. By depositing the payment at the beginning rather than at the end of the year, it has ???? year of compounding.

3. Loan interest deductions
Challenge
a. PMT &#61501; \$10,000 &#61624; (PVIFA13%,3)
PMT &#61501; \$10,000 &#61624; (2.361)
PMT &#61501; \$??
Calculator solution: \$??

b.
End of
Year Loan
Payment Beginning of
Year Principal Payments End of Year
Principal
Interest Principal
1 \$4,235.49 \$10,000.00 \$1,300.00 \$2,935.49 \$7,064.51
2 4,235.49 7,064.51 918.39 3,317.10 3,747.41
3 ?? ?? ?? ?? ??
(The difference in the last year'

#### Solution Preview

1. Present value calculation:
A PVIF  1  (1  0.02)4  ?? 0.9238
B PVIF  1  (1  0.10)2  ?? 0.8264
C PVIF  1  (1  0.05)3  ?? 0.8638
D PVIF  1  (1  0.13)2  ?? 0.7831

2. Future value of an annuity
a. Future value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity (2) Annuity Due
FVAk%,n  PMT(FVIFAk%,n) FVAdue  PMT[(FVIFAk%,n(1  k)]
A FVA8%,10  \$2,50014.487 FVAdue  \$2,500(14.4871.08)
FVA8%,10  \$?? 36,217.5 FVAdue ...

#### Solution Summary

The solution explains some calculations using time value of money.

\$2.19