Question 4.P.8: Repeat Problem 4.7 using daily compounding. For computationa......
Repeat Problem 4.7 using daily compounding. For computational simplicity, assume 30 days in each month (many banks do this).
Step-by-Step
Here, r = 10%/12 = 0.00833333 and α = 30; hence by (4.2), the effective monthly interest rate is
i = \left(1 + \frac{r}{\alpha}\right)^{\alpha} – 1 (4.2) \\\\\ i = \left(1 + \frac{0.00833333}{30}\right)^{30} – 1 = 0.0083670Now use (2.7), as before.
P/A = (A/P)^{-1} = \frac{ (1 + i)^n – 1 }{i(1 + i)"} – \frac{1 – (1 + i)^{-n}}{1} (2.7) \\\\ P = \$500\frac{(1 + 0.0083670)^{(12)(10)} – 1}{(0.0083670)(1 + 0.0083670)^{(12)(10)}} = \$500\frac{1.717909}{(0.0083670)(2.717909)} = \$37 771.61Related Answered Questions
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