quiz3 solutions QRMS - PMT = $15 , 000 ( . 055 12 ) ( 1 + ....

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Math 1012: QRMS Quiz 3 Mar. 2, 2012 Name: 4B 69 Use the formula for continuous compounding to compute the balance in the following account after 5 years. Also, find the APY for the account. A $7000 dollar deposit in an account with an APR of 4.5%. Solution: Using the formula for continuous compounding we compute: A = P × e (APR × Y ) = $7 , 000 × e (0 . 045 × 5) $8 , 766 . 26 . Now applying the formula for APY in the case of continuous compounding we compute: APY = e APY - 1 = e 0 . 045 - 1 0 . 046 = 4 . 6% . 4C 33 You want to purchase a new car in 3 years and expect the car to cost $15,000. Your bank offers a savings plan with a guaranteed APR of 5.5% if you make monthly payments. How much should you deposit each month to end up with $15,000 in 3 years? Solution: We need to solve the savings plan formula for PMT: A = PMT × h ( 1 + APR n ) nY - 1 i ( APR n ) m PMT = A × ( APR n ) ( 1 + APR n ) nY - 1 Now plugging in the given information gives:
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Unformatted text preview: PMT = $15 , 000 ( . 055 12 ) ( 1 + . 055 12 ) 12 3-1 $384 . 19 . 1 Math 1012: QRMS Quiz 3 Mar. 2, 2012 4D 45 Suppose you have a student loan of $30,000 with an APR of 9% for 20 years. Suppose you would like to pay o the loan in 10 years instead of 20. What monthly payments will you need to make? Solution: Using the formula for loan payments with monthly compounding we compute: PMT = P ( APR n ) 1-( 1 + APR n )-nY = $30 , 000 ( . 09 12 ) 1-( 1 + . 09 12 )-12 10 $380 . 03 . Note that we are using Y = 10 since were trying to pay of the loan in 10 years, even though the original loan term is 20 years. This reduces the total amount of interest paid over the duration of the loan. 2...
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quiz3 solutions QRMS - PMT = $15 , 000 ( . 055 12 ) ( 1 + ....

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