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MATH 320 HW 5

# MATH 320 HW 5 - i what would the accumulated value of these...

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MATH 320 HOMEWORK 5 Due Wednesday, September 29 1. A perpetuity pays 1 at the end of every year plus an additional 1 at the end of every second year. The present value of the perpetuity is K for i 0 . Determine K in terms of i (simplify!) 2. Annual deposits of 10 are made into a fund for 20 years. 21 years after the last deposit, payment of X is made from the fund. This payment is repeated annually forever. Find the annual interest rate, if X = 258 . 3. A person deposits 100 at the beginning of each year for 20 years. Sim- ple interest at an annual rate of i is credited to each deposit from the date of deposit, to the end of 20-year period. The total amount thus accumulated (at the end of 20-year period) is 2840. If instead, com- pound interest had been credited at an eﬀective annual rate of
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Unformatted text preview: i , what would the accumulated value of these deposits have been at the end of 20 years? 4. I borrow 500 from the bank at time 0, at an interest rate of 0.10 per annum eﬀective. I am to repay the loan by n-1 annual installments of X , followed by a drop payment at time n of less then X. (a) If X = 80 , ±nd n and the value of the drop payment. (b) What happens if X = 30? What is the smallest possible value of X ? 5. A sum, P, is used to buy a deferred perpetuity-due of 1 payable an-nually. The eﬀective annual rate of interest is i, i > . Calculate the deferred period. Show work! (A) ln( P d ) (B) 1-ln( iP ) δ (C)-ln( iP ) δ (D) 1 + ln( dP ) δ (E) ln( dP ) δ . 1...
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