There are three versions of this quiz. Find your version.

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1 There are three verion of thi quiz. Find your verion.

2 MATH 373 Quiz 3 Spring 2018 February 13, Tyler purchae a US Treaury Bill that mature for 15,000 in 150 day. The Quoted Rate on thi US Treaury Bill i 8.25%. Determine the annual effective interet rate that Tyler will earn on the US Treaury Bill. Your anwer hould be accurate to five decimal place. 360 Maturity Value Price Quoted Rate Number of Day Maturity Value ,000 Price , 000 Price (15, 000) , Price 15, , (14, )(1 i) 15, , i i ,

3 2. Emily make a loan of 100,000 to the US Government. Under the loan, the US Government will pay an annual rate of 3.5% compounded continuouly plu the annual rate of inflation each year compounded continuouly. Since US Government i conidered a rik free borrower, there i no charge for default. The annual rate of inflation compounded continuouly i 2.3% during the firt year, 4.2% during the econd year, and x % during the third year. At the end of three year, Emily receive a payment of 124, to repay the loan. Determine x. Your anwer hould be accurate to five decimal place. ( x/100) (100, 000) e 124, e (0.17 x/100) x /100 ln( ) x 4.8%

4 3. Brinker Bank make 4 year loan to college tudent. Brinker want to receive an annual rate of 2.5% compounded continuouly to compenate for deferred conumption. Additionally, Brinker expect that inflation will occur at an annual rate of 3.1% compounded continuouly over the next four year. However, ince the inflation rate could be higher, Brinker would like to receive an annual rate of 0.25% compounded continuouly a compenation for the inflation rik. Additionally, Brinker expect 5% of the loan to default with a loan recovery rate of 42%. Determine the annual rate compounded continuouly that Brinker hould charge for default. Your anwer hould be accurate to five decimal place. Total Rate Deired Each Year (4)(0.0585) (4)( ) (4)( ) e (1 0.05) e (0.05)(0.42) e e (4)( ) ln (4)( )

5 MATH 373 Quiz 3 Spring 2018 February 13, Emily make a loan of 100,000 to the US Government. Under the loan, the US Government will pay an annual rate of 2.3% compounded continuouly plu the annual rate of inflation each year compounded continuouly. Since US Government i conidered a rik free borrower, there i no charge for default. The annual rate of inflation compounded continuouly i 3.5% during the firt year, 4.2% during the econd year, and x % during the third year. At the end of three year, Emily receive a payment of 120, to repay the loan. Determine x. Your anwer hould be accurate to five decimal place. ( x/100) (100, 000) e 120, e (0.146 x/100) x /100 ln( ) x 3.8%

6 2. Brinker Bank make 4 year loan to college tudent. Brinker want to receive an annual rate of 3.5% compounded continuouly to compenate for deferred conumption. Additionally, Brinker expect that inflation will occur at an annual rate of 2.9% compounded continuouly over the next four year. However, ince the inflation rate could be higher, Brinker would like to receive an annual rate of 0.50% compounded continuouly a compenation for the inflation rik. Additionally, Brinker expect 4% of the loan to default with a loan recovery rate of 58%. Determine the annual rate compounded continuouly that Brinker hould charge for default. Your anwer hould be accurate to five decimal place. Total Rate Deired Each Year (4)(0.069) (4)(0.069 ) (4)(0.069 ) e (1 0.04) e (0.04)(0.58) e e (4)(0.069 ) ln (4)(0.069 )

7 3. Tyler purchae a US Treaury Bill that mature for 20,000 in 210 day. The Quoted Rate on thi US Treaury Bill i 7.30%. Determine the annual effective interet rate that Tyler will earn on the US Treaury Bill. Your anwer hould be accurate to five decimal place. 360 Maturity Value Price Quoted Rate Number of Day Maturity Value ,000 Price , 000 Price (20, 000) , Price 20, , (19, )(1 i) 20, , i i ,

8 MATH 373 Quiz 3 Spring 2018 February 13, Brinker Bank make 4 year loan to college tudent. Brinker want to receive an annual rate of 2.1% compounded continuouly to compenate for deferred conumption. Additionally, Brinker expect that inflation will occur at an annual rate of 2.8% compounded continuouly over the next four year. However, ince the inflation rate could be higher, Brinker would like to receive an annual rate of 0.35% compounded continuouly a compenation for the inflation rik. Additionally, Brinker expect 6% of the loan to default with a loan recovery rate of 64%. Determine the annual rate compounded continuouly that Brinker hould charge for default. Your anwer hould be accurate to five decimal place. Total Rate Deired Each Year (4)(0.0525) (4)( ) (4)( ) e (1 0.06) e (0.06)(0.64) e e (4)( ) ln (4)( )

9 2. Tyler purchae a US Treaury Bill that mature for 25,000 in 270 day. The Quoted Rate on thi US Treaury Bill i 8.75%. Determine the annual effective interet rate that Tyler will earn on the US Treaury Bill. Your anwer hould be accurate to five decimal place. 360 Maturity Value Price Quoted Rate Number of Day Maturity Value ,000 Price , 000 Price (25, 000) , Price 25, , (23, )(1 i) 25, , i i ,

10 3. Emily make a loan of 100,000 to the US Government. Under the loan, the US Government will pay an annual rate of 4.5% compounded continuouly plu the annual rate of inflation each year compounded continuouly. Since US Government i conidered a rik free borrower, there i no charge for default. The annual rate of inflation compounded continuouly i 1.2% during the firt year, 2.2% during the econd year, and x % during the third year. At the end of three year, Emily receive a payment of 123, to repay the loan. Determine x. Your anwer hould be accurate to five decimal place. ( x/100) (100, 000) e 123, e (0.169 x/100) x /100 ln( ) x 4.3%