Exam+1B+Solutions

Exam+1B+Solutions - ISyE 3025 Professor Nagi Gebraeel...

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Engineering Economy Spring 2011 Professor Nagi Gebraeel Solution to Exam 1B 1. An individual contributes $200 per month to a “401(k)” retirement account. The account earns interest at a nominal interest rate of 8% compounded monthly (i.e. interest is credited monthly). What is the value of the account after 35 years? (a) $310 , 000 (b) $368 , 000 (c) $414 , 000 (d) $447 , 000 (e) $459 , 000 X Solution: This cash flow stream can be modeled as an annuity over 35 × 12 months with an interest rate of 8% / 12 and a payment of $200 per period. The future value of this stream is calculated as follows: F = A [(1 + i ) N - 1] i = 200[(1 + . 08 / 12) 35 × 12 - 1] . 08 / 12 = $458 , 776 . 2. Money invested at annual nominal interest rate of 6% compounded monthly will triple in approximately how many months? (a) 220 X (b) 19 (c) 57 (d) 113 Solution: The monthly interest rate is 6% / 12. One way to think about this problem is to hypotheti- cally make a deposit of $1 at time 0 and let it grow for N months until it reaches a future value of $3. Use the equation for F/P and solve for N as follows: F = P (1 + i ) N 3 = 1 × (1 + . 06 / 12) N ln 3 = N ln(1 + . 06 / 12) N = 220 . 27 . 3. Fifteen years ago, $1000 was deposited in a bank account, and today it is worth $2370. The bank pays interest semi-annually. What was the nominal annual interest rate paid on this account? (a) 5
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Exam+1B+Solutions - ISyE 3025 Professor Nagi Gebraeel...

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