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1 AK/ADMS 3530.03 Finance Midterm Exam Solutions Type A Exam Numerical Questions (4 points each) 1. (Q.2 in B) What is the APR on a loan with an effective annual rate of 15.01% and weekly compounding of interest? (There are 52 weeks in a year.) A) 13.00% B) 13.50% C) 14.00% D) 14.50% Answer C %. 14 52 002693 . 0 m rate weekly APR %. 2693 . 0 1 ) 1501 . 0 1 ( 1 ) EAR 1 ( rate interest weekly The 52 / 1 m / 1 = × = × = = + = + = 2. (Q. 1 in B) You are indifferent to the following two accounts: an account with a 2.5% quarterly interest rate and an account paying a X% semi-annual interest rate. What is X? A) 5.0000% B) 5.0625% C) 5.1906% D) 5.2200% Answer B %. 0625 . 5 1 ) 103813 . 0 1 ( 1 ) EAR 1 ( r %. 3813 . 10 1 ) 025 . 0 1 ( 1 ) r 1 ( EAR 2 / 1 m / 1 2 4 m 1 2 1 = + = + = = + = + = 3. (Q. 7 in B) In two years from today, the following cash flows will have a future value of \$7,651.25: \$500 today, \$Y at the end of one year, and \$5,000 at the end of two years. The annual interest rate is 5%. What is Y? A) \$1,822.44 B) \$1,850.00 C) \$2,000.00 D) \$2,126.25 Answer C

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2 . 2000 \$ Y 25 . 7651 \$ 5000 \$ ) 05 . 1 ( Y 25 . 551 \$ ) 05 . 0 1 ( 5000 \$ ) 05 . 0 1 ( Y ) 05 . 0 1 ( 500 \$ ) r 1 ( CF ) r 1 ( Y ) r 1 ( CF FV 0 1 2 t 3 t t 1 3 2 1 = = + + = + + + + + = + + + + + = 4. (Q. 8 in B) A cash-strapped young man offers to buy your car with four, equal end-of- year payments of \$3,000, beginning three years from today. Assuming that you are indifferent to cash versus credit, that you can invest at 10% annually, and that you want to receive \$8,000 for the car, should you accept his offer? A) Yes; present value is \$8,645. B) Yes; present value is \$9,510. C) No; present value is \$7,145. D) No; present value is \$7,859. Answer D . 17 . 7859 \$ ) 1 . 0 1 ( 60 . 9509 \$ ) 1 . 0 1 ( ] ) 1 . 0 1 ( 1 . 0 1 1 . 0 1 [ 3000 \$ ) r 1 ( ] ) r 1 ( r 1 r 1 [ C : is offer the of value present The 2 2 4 t t 2 1 = + = + + = + + 5. (Q. 9 in B) You decide to deposit \$200 at the end of each month for the first year and deposit \$400 at the end of every month during the second year. The annual interest rate is 12% and deposits will begin in one month from today. How much money can you accumulate in two years? A) \$7,587.91 B) \$7,891.43 C) \$7,931.19 D) \$8,000.00 Answer B
3 . 43 . 7891 \$ ] 009489 . 0 1 ) 009489 . 0 1 ( [ 400 \$ ) 009489 . 1 ]( 009489 . 0 1 ) 009489 . 0 1 ( [ 200 \$ ] r 1 ) r 1 ( [ C ) r 1 ]( r 1 ) r 1 ( [ C FV %. 9489 . 0 1 ) 12 . 0 1 ( 1 ) EAR 1 ( ) r ( rate erest int Monthly 12 12 12 t 2 t t 1 12 / 1 t / 1 = + + + = + + + + = = + = + = 6. (Q. 3 in B) A house is selling at \$350,000 (assuming no down payment). The current mortgage rate is 7% (APR, semi-annual compounding). Assuming a 25-year amortization and bi-weekly mortgage payments, how much principal will be paid in the first 5 years of the mortgage life? (There are 26 two-weeks in a year.) A) \$30,500.00 B) \$31,339.89 C) \$318,660.11 D) \$319,112.38 Answer B The EAR is: %. 1225 . 7 1 ) 2 07 . 0 1 ( 1 ) 2 APR 1 ( EAR 2 2 = + = + = The bi-weekly rate is: %. 2650 . 0 1 ) 071225 . 0 1 ( 1 ) EAR 1 ( r 26 / 1 m / 1 = + = + = The bi-weekly mortgage payment is: . 76 . 1129 \$ 80 . 309 350000 PMT 80 . 309 PMT ] ) 00265 . 1 ( 00265 . 0 1 00265 . 0 1 [ PMT ] ) r 1 ( r 1 r 1 [ PMT 350000 \$ 25 26 t = = × = = + = × The principal reduction in the first 5 years is: . 89 . 31339 \$ 11 . 318660 \$ 350000 \$ 06 . 282 76 . 1129 \$ 350000 \$ ] ) 00265 . 1 ( 00265 . 0

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