ACTSC 231 Tutorial02

# ACTSC 231 Tutorial02 - What minimum nominal annual rate...

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Problem Set 2: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. A loan of face amount X , due in one-half year, is valued \$4,992 today. Find X under each of the following interest calculation methods. (a) Compound interest at eﬀective annual rate 8% (b) Simple interest at annual rate 8% (c) Compound discount at eﬀective annual rate 8% (d) Simple discount at annual rate 8% Q2. Roy deposits \$10 into a fund today and \$20 ﬁfteen years later. Interest is credited at a nominal discount rate of d (4) compounded quarterly for the ﬁrst 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is \$100. Calculate d (4) . Q3. Simplify the following expression (in terms of the annual eﬀective interest rate i only). ± 1 + i (2) 2 ²± 1 + i (3) 3 ²± 1 + i (6) 6 ² ± 1 - d (2) 2 ²± 1 - d (3) 3 ²± 1 - d (6) 6 ² Q4. Bank A pays interest at rate i (2) = 15%. Bank B pays interest compounded daily.
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Unformatted text preview: What minimum nominal annual rate must Bank B pay in order to be as attractive as Bank A? Assume we have 365 days in one year. Q5. If the eﬀective annual rate of discount is 8%, for how long do you need to invest a principal of \$500 so that it will accumulate to \$750? Q6. Consider a 4-year investment with an annual simple discount rate of 10%. Find the equivalent annual simple interest rate i over the same investment period. Q7. Latisha wishes to obtain \$4,000 to pay her college tuition now. She qualiﬁes for a loan with a level annual eﬀective discount rate of 3.5%. (a) How much will she have to repay if the loan term is six years? (b) What is the annual eﬀective interest rate of Latisha’s loan? Q8. Suppose we have compound interest and an eﬀective monthly interest rate of 0.5%. Find equivalent rates i (12) , i , and d . 1...
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