ACTSC 231 Tutorial05

# ACTSC 231 Tutorial05 - Problem Set 5 ACTSC 231 Mathematics...

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Problem Set 5: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. A deferred perpetuity-due begins payments at time n with annual payments of \$1,000 per year. If the present value of this perpetuity-due is equal to \$6,561 and the effective rate of interest i = 1 / 9, find n . Q2. A loan of \$50,000 is made at time 0 and is repaid by making regular annual payments of \$7426.39 for 8 years in total. (a) What is the outstanding loan balance at the end of three years? (b) What is the interest payment included in the fourth regular payment? Q3. Julia borrows \$10,000 and repays the loan by making annual (end of the year) payments of X for 5 years. The annual effective rate on the loan is 6%. (a) Determine P and the outstanding loan balance at the end of two years. (b) Julia skips the third payment. What additional payment does she need to make at time 5 in order to repay the loan within 5 years, as originally planned? Q4. Annual deposits are made into a fund at the beginning of each year for 10 years. The first 5 deposits are \$1,000 each and deposits increase by 5% per year thereafter. If the
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