MA170wk3solns

# Accumulated value of the payments 80 1 0 08 8 12 35 1

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Accumulated value of the payments: 80 ° 1 + 0 : 08 ° 8 12 ±± + 35 ° 1 + 0 : 08 ° 3 12 ±± + 150 ° 1 + 0 : 08 ° 2 12 ±± : = \$271 : 97 ) the balance at the due date is X = 1288 ° 271 : 97 = \$1016 : 03 1

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2. [6 marks ] Vivian took a \$5000 discounted loan from a bank that uses a simple discount rate of 10% on July 12, 2010. The loan must be repaid to the bank no later than January 10, 2011. (a) How much money does Vivian receive from the bank on the day of her loan? # of days between July 12, 2010 and January 10, 2011: 365 ° 193 + 10 = 182 P = 5000 ° 1 ° 0 : 1 ° 182 365 ±± = \$4750 : 68 (b) How large a loan should she have requested if she requires exactly \$5000 immediately? 5000 = S ° 1 ° 0 : 1 ° 182 365 ±± ) S = 5000 ° 1 ° 0 : 1 ° 182 365 ±± = \$5262 : 40 (c) Determine the simple interest rate that is equivalent to the discount rate charged on the loan. Express the rate as percentage to two decimal places. ° 1 ° 0 : 1 ° 182 365 ±± = ° 1 + r ° 182 365 ±± ° 1 ) 1 + r ° 182 365 ± = ° 1 ° 0 : 1 ° 182 365 ±± ° 1 ) r = ° 365 182 ± ° 1 ° 0 : 1 ° 182 365 ±± ° 1 ° 1 ! : = 0 : 105 25 = 10 : 53% 3. [5 marks ] A promissory note with a face value of \$2000 and a term of 120 days bears an annual interest rate of 10%. The note is sold 30 days after it is written to a bank that discounts at a simple discount rate. (a) If the bank will pay \$2040 for the note, what is the simple discount rate?
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