Chapter Three Compound Interest 2 Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

3 5 Finding the Compound Rate : Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

4 Example 5.1 page 154 For a sum of money to double in 8 years, at what rate must it compound quarterly? We do not need to know the sum of money, just that S = 2P. Quarterly interest means that the number of conversions periods n = 8 × 4 = 32. Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

5 Example 5.2 page 154 If the population of a city increased from 23,480 in 1980 to 42,650 in 1998, what was the annual rate of increase? Eighteen years pass from.1980 to Since the compounding is annual, n = 18. Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

6 Example 5.3 page 155 If an investment increased from $18,000 to $21,410 in 2 years and 6 months, find the rate of increase compounded quarterly. The number of interest periods n = 2.5 × 4 = 10. If you are computing n or i, most financial calculators want the present value and future value to be opposite signs. Enter the information as follows: n = 10, PV = - 18,000, FV = 21,410. Compute i. Answer = This is the quarterly rate, so multiply by 4 to get or 7%(4). Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

7 Example 5.4 page 155 A fund increased 85% during the last 5 years. Find the annual compounded rate of increase. If the original principal was P, then the balance in the fund after 5 years is expressed by S = P +.85P. By factoring, we find that S = P(l +.85) = P(1.85). Using the calculator, we can let PV = -1 and FV = 1.85, while n = 5. The computed annual rate is 13.09%(1). Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

8 Example 5.5 page 155 A fund increased 175% during a 10-year period. Find the semiannual compounded rate of increase. Apply the same method as in Example 3.5.4: S = P P = P(2.75). Using the FIN mode, let PV = -1 and FV = 2.75, while n = 20. Compute i to get 10.38%(2). Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

9 Exercise 7 Page 156 At what rate converted monthly is $200 worth $500 in 4 years? Express the answer as a rate per month and as a nominal rate. Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

10 Exercise 11 page 156 At what rate converted quarterly could Bertram's bank account increase by 60% in just 2 years? Express the answer as a rate per quarter and as a nominal rate. Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

11 Exercise 13 page 156 A city grew from 100 people in 1900 to 3400 in Find the rate of growth. Predict the city population in 2010 assuming the same rate of growth. Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

12 Exercise 23 page 157 Find the nominal discount rate compounded semiannually that will accumulate the fallowing invested sums to $2000 in 4 years: $500 current value, $400 in 2 years and $800 in 4 years. 500(1 – d) (1 – d) = 2000 d = % / half-year → d(2) = 8.91%(2) Instructors: Lobna M Farid Copy rights for Gary C. Guthnie Larry D. Leman, Mathematics of Interest Rates and Finance

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