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MATH 320 HW 3 - of 20 for the ±rst two years and a force...

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MATH 320 HOMEWORK 3 Due Wednesday, September 15 1. Annual compound interest rates are 13% in 1984, 11% in 1985, and 15% in 1986. Find the effective rate of compound interest per year which yields an equivalent return over the three-year period. 2. suppose that δ t = . 04(1 + t ) - 1 . (a) Find a ( t ) (b) I invest 10 at t = 2. What is the value of my investment at t = 5? 3. Two funds, X and Y, start with the same amount. Fund X accumulates at force of interest of 10%. Fund Y accumulates at a rate of interest i , compounded semiannually. At the end of 10 years, fund X is 1.1 times as big as fund Y. Calculate i . 4. Steve puts 100 into a fund that pays an effective annual rate of discount
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Unformatted text preview: of 20% for the ±rst two years, and a force of interest of rate δ t = 2 t/ ( t 2 + 8), 2 ≤ t ≤ 4, for the next 2 years. At the end of four years, the amount in Steve’s account is the same as it would have been had he put 100 into an account paying interest at a nominal rate of j per annum compounded quarterly for four years. Calculate j . 5. I borrow 100 at an annual interest rate of j compounded semiannually. Six months later, the annual interest rate (compounded semiannually) suddenly goes up by 4%. One year after the loan, I owe 110.24. Find j . 1...
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