MATH 373 Quiz 3 Fall 2017 October 12, 2017
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1 MATH 373 Quz 3 Fall 2017 October, Alex wants to nvest for hs retrement. Today s hs 22 nd brthday. He wll make a payment of 10,000 on each brthday begnnng wth hs 30 th brthday. Hs last payment wll be on hs 64 th brthday. Alex earns an annual effectve nterest rate of 6%. Calculate the amount that Alex wll have at the age 65. Soluton: Frst, we note that the number of payments s 35. Second, we note that we want the accumulated value at age 65 whch s one perod after the last payment at age (1.06) 1 Answer (10, 000) s (10, 000) (1.06) 1,104, Copyrght Jeffrey Beckley 2017
2 2. Alan buys a house for 300,000. He fnances the entre amount wth a mortgage. The mortgage requres monthly payments for 30 years. The nterest rate on the mortgage s an annual effectve nterest rate of 9%. Calculate Alan s monthly payment. Soluton: Payments are monthly so we need the monthly effectve nterest rate but we are gven the annual effectve nterest rate. () () 1/ (1.09) Qa , , 000 Q ( ) Copyrght Jeffrey Beckley 2017
3 3. A perpetuty due has a present value of 25,000 and makes quarterly payment of 500 per quarter. Calculate the annual effectve nterest rate used to calculate the present value. Soluton: (500) (1 ) 25, , ,500 24,500 But snce payments are quarterly, the above rate s a quarterly effectve rate. We need the annual effectve rate. (4) (1 ) ,500 Copyrght Jeffrey Beckley 2017
4 MATH 373 Quz 3 Fall 2017 October, A perpetuty due has a present value of 26,000 and makes quarterly payment of 500 per quarter. Calculate the annual effectve nterest rate used to calculate the present value. Soluton: (500) (1 ) 26, , ,500 25,500 But snce payments are quarterly, the above rate s a quarterly effectve rate. We need the annual effectve rate. (4) (1 ) ,500 Copyrght Jeffrey Beckley 2017
5 2. Alex wants to nvest for hs retrement. Today s hs 21 nd brthday. He wll make a payment of 10,000 on each brthday begnnng wth hs 30 th brthday. Hs last payment wll be on hs 64 th brthday. Alex earns an annual effectve nterest rate of 7%. Calculate the amount that Alex wll have at the age 65. Soluton: Frst, we note that the number of payments s 35. Second, we note that we want the accumulated value at age 65 whch s one perod after the last payment at age (1.07) 1 Answer (10, 000) s (10, 000) (1.07) 1, 479, Copyrght Jeffrey Beckley 2017
6 3. Alan buys a house for 300,000. He fnances the entre amount wth a mortgage. The mortgage requres monthly payments for 20 years. The nterest rate on the mortgage s an annual effectve nterest rate of 6%. Calculate Alan s monthly payment. Soluton: Payments are monthly so we need the monthly effectve nterest rate but we are gven the annual effectve nterest rate. () () 1/ (1.06) Qa , , 000 Q ( ) Copyrght Jeffrey Beckley 2017
7 MATH 373 Quz 3 Fall 2017 October, Alan buys a house for 200,000. He fnances the entre amount wth a mortgage. The mortgage requres monthly payments for 25 years. The nterest rate on the mortgage s an annual effectve nterest rate of 7.2%. Calculate Alan s monthly payment. Soluton: Payments are monthly so we need the monthly effectve nterest rate but we are gven the annual effectve nterest rate. () () 1/ (1.072) Qa , , 000 Q ( ) Copyrght Jeffrey Beckley 2017
8 2. A perpetuty due has a present value of 24,000 and makes quarterly payment of 500 per quarter. Calculate the annual effectve nterest rate used to calculate the present value. Soluton: (500) (1 ) 24, , ,500 23,500 But snce payments are quarterly, the above rate s a quarterly effectve rate. We need the annual effectve rate. (4) (1 ) ,500 Copyrght Jeffrey Beckley 2017
9 3. Alex wants to nvest for hs retrement. Today s hs 20 nd brthday. He wll make a payment of 10,000 on each brthday begnnng wth hs 30 th brthday. Hs last payment wll be on hs 64 th brthday. Alex earns an annual effectve nterest rate of 8%. Calculate the amount that Alex wll have at the age 65. Soluton: Frst, we note that the number of payments s 35. Second, we note that we want the accumulated value at age 65 whch s one perod after the last payment at age (1.08) 1 Answer (10, 000) s (10, 000) (1.08) 1,861, Copyrght Jeffrey Beckley 2017
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