MA170wk5solns

# Use 2 decimal places for the interest rate real rate

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taking in°ation into account? Use 2 decimal places for the interest rate. Real rate of interest: i ° r 1 + r = 0 : 0386 ° 0 : 0207 1 + 0 : 0207 : = 0 : 01753698442 : = 1 : 75% (e) Suppose that the interest earned on the bond is taxable at a rate of 40%. (Interest earnings are often taxable at the investor’s marginal tax rate. Here we will assume that rate is 40%.) : Suppose further that an investor had the option in 2000 to invest in a tax-sheltered investment offering an interest rate of j 12 = 2 : 4% : Determine the real annual interest rates for each option taking the in°ation rate and the tax rate (where appropriate) into consideration. Based on your calculations, which option is better? Real rate for the bond: 0 : 0386 (0 : 6) ° 0 : 0207 1 + 0 : 0207 : = 0 : 002410110708 : = 0 : 24% 1 + j = ° 1 + 0 : 024 12 ± 12 ) j = ° 1 + 0 : 024 12 ± 12 ° 1 : = 0 : 024265768 i real = 0 : 024265768 ° 0 : 0207 1 + 0 : 0207 : = 0 : 00349345351 : = 0 : 35% The tax-sheltered option is the better option. 2

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3. [6 marks ] Anika lends an acquaintance \$800 with the following terms: \$150 to be repaid in four months ; \$200 to be repaid in six months, \$275 to be repaid in eight months and \$250 to be repaid in 11 months. Assume that interest is compounded monthly. Use a time diagram and the given focal dates to construct an appropriate equation of value with unknown j 12 . Do not try to solve the equations for j 12 : (a) focal date = date of the loan; 800 = 150 ° 1 + j 12 12 ± ° 4 + 200 ° 1 + j 12 12 ± ° 6 + 275 ° 1 + j 12 12 ± ° 8 + 250 ° 1 + j 12 12 ± ° 11 (b) focal date = 7 months from the date of the loan. 800 ° 1 + j 12 12 ± 7 = 150 ° 1 + j 12 12 ± 3 + 200 ° 1 + j 12 12 ± + 275 ° 1 + j 12 12 ± ° 1 + 250 ° 1 + j 12 12 ± ° 4 4. [5 marks ] Jack has two loans to repay. The ±rst loan, which accrues interest at j 12 = 12%
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