# Eco/365 Week 4

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------------------------------------------------- - 1 of 7 ACST201.A1.001 A \$100,000 Bank Bill will mature at the end of 133 days. Find its price, to the nearest cent, assuming: a)9% pa simple interest and a 365 day year. Price = \$ b)9% pa simple discount and a 365 day year. Price = \$ c)9% pa simple interest and a 360 day year. Price = \$ d)9% pa simple discount and a 360 day year. Price = \$ ------------------------------------------------- - Feedback a)You are correct. The data can be displayed on a time line as follows: | | | \$100,000 | | | 0 | 133 | \$P | | | | P | = | Price | = | unknown | | S | = | Face value | = | \$100,000 | | r | = | Simple interest rate (decimal) | = | 9 |…show more content…
| | | = | \$787,526.87 | Rounded as last step | b)This is not correct. The investor sold the security 39 days later. To calculate the sale price, the maturity value of the Note must be discounted from its maturity date back to the date of sale. The period of the time line that we are interested in is from the maturity date (time 123 days) back to the sale date (time 39 days). Note also that the interest rate we must use is a simple discount rate. The data can be displayed on a time line. | | | | | \$800,000 | | | | 0 | 39 | 123 | | \$P | | | | | P | = | Price | = | unknown | | S | = | Face value | = | \$800,000 | | d | = | Simple discount rate (decimal) | = | 4.7 | 100 | | = | 0.047 | | t | = | Time period (years) | = | 84 | 365 | | = | 0.23013699... years | | The step-by-step calculation is: P | = | S(1 - dt) | | | = | 800,000(1 - 0.047 x 0.23013699...) | | | = | 800,000 x 0.98918356... | | | = | \$791,346.85 | Rounded as last step | c)This is not…show more content…
years. | | The step-by-step calculation is: P | = | S(1 + rt)-1 | | | = | 400,000(1 + 0.0892 x 0.24657534...)-1 | | | = | 400,000 x 0.97847883... | | | = | \$391,391.53 | Rounded as last step | b)You are correct. When the first bill matures at time 90 days, the investor purchases a second bill. We must find the purchase price of the second bill. This can be displayed on a time line: | | | | | \$P | \$400,000 | | | | | | 0 | 90 | 180 | 270 | | | | | | | | | P | = | price | = | unknown | | S | = | Maturity value | = | \$400,000 | | r | = | Simple interest rate (decimal) | = | 9.16 | 100 | | = | 0.0916 | | t | = | Time period (years) | = | 90 | 365 | | = | 0.24657534... years. | | The step-by-step calculation is: P | = | S(1 + rt)-1 | | = | 400,000(1 + 0.0916 x 0.24657534...)-1 | | = | 400,000 x 0.97791257...