Revision as of 21:55, 18 November 2023 by Admin (Created page with "'''Solution: B''' Monthly payment at time t is <math>1000(0.98)^{t-1}</math> Because the loan amount is unknown, the outstanding balance must be calculated prospectively. The value at time 40 months is the present value of payments from time 41 to time 60: <math display = "block"> \begin{array}{c}{{O B_{40}=1000[0.98^{40} v^{1}+\cdots+0.98^{59} v^{20}]}}\\ {{=1000\frac{0.98^{40} v^{1}-0.98^{60} v^{21}}{1-0.98 v}, v=1/(1.0075)}}\\ {{=10000\frac{0.44238-0.25434}{1-0.972...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: B
Monthly payment at time t is [math]1000(0.98)^{t-1}[/math]
Because the loan amount is unknown, the outstanding balance must be calculated prospectively. The value at time 40 months is the present value of payments from time 41 to time 60:
[[math]]
\begin{array}{c}{{O B_{40}=1000[0.98^{40} v^{1}+\cdots+0.98^{59} v^{20}]}}\\ {{=1000\frac{0.98^{40} v^{1}-0.98^{60} v^{21}}{1-0.98 v}, v=1/(1.0075)}}\\ {{=10000\frac{0.44238-0.25434}{1-0.97270}=688.}}\end{array}
[[/math]]
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