Question

Chapter 5 Time Value of Money 179 ermediate blems 5-9 5-10 PRESENT AND FUTURE VALUES FOR DIFFERENT PERIODS Find the following values using the ators and then a financial calculator Compounding/discounting occurs annually. a. An initial $600 compounded for 1 year at 6% b. An initial $600 compounded for 2 years at 6% c. The present value of $600 due in 1 year at a discount rate of 6% d. The present value of $600 due in 2 years at a discount rate of 6% PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES Find the following values. Compounding/discounting occurs annually. a. An initial $200 compounded for 10 years at 4% b. An initial 5200 compounded for 10 years at c. The present value of $200 due in 10 years at 4% d. The present value of $1,80 due in 10 years at 8% and at 4% e. Define present male and illustrate it using a time line with data from part d. How are present values affected by interest rates? GROWTH RATES Sawyer Corporation's 2015 sales were 55 million. Its 2010 sales were $2.5 million 5-11 5-12 a. At what rate have sales been growing? b. Suppose someone made this statement: "Sales doubled in 5 years. This represents a growth of 100% in 5 years, so dividing 100% by 5, we find the growth rate to be 20% per year." Is the statement correct? EFFECTIVE RATE OF INTEREST Find the interest rates earned on each of the following: a. You borre 5720 and promise to pay back $792 at the end of 1 year b. You lend $720 and the borrower promises to pay you $792 at the end of 1 year. c. You borrow $65,000 and promise to pay back 998,319 at the end of 14 years d. You borrow $15,000 and promise to make payments of S4,058.60 at the end of each year for 5 years. TIME FOR A LUMP SUM TO DOUBLE How long will it take $300 to double if it ears the following rates? Compounding occurs once a year. 5-13 b. 13% c. 21% d. 100% 5-14 FUTURE VALUE OF AN ANNUITY Find the future tules of these ordinary condities Compounding occurs once a year. a. $500 per year for 8 years at 14% b. $250 per year for 4 years at 7% c. $700 per year for 4 years at 0% d. Rework parts a, b, and c assuming they are ammunities due. 5-15 PRESENT VALUE OF AN ANNUITY Find the present values of these ordinary annuities. Discounting occurs once a year. a. $600 per year for 12 years at 8% b. $300 per year for 6 years at 4% c. $500 per year for 6 years at 0% d. Rework parts a, b, and c assuming they are annuities due. 5-16 PRESENT VALUE OF A PERPETUITY What is the present value of a $600 perpetuity if the interest rate is 5%? If interest rates doubled to 10%, what would its present value be? 5-17 EFFECTIVE INTEREST RATE You borrow $230,000; the annual loan payments are $20,430.31 for 30 years. What interest rate are you being charged?

Answer 1

A В C D E G н K L M 5.10(a) 1 given 5.9 (a) 200 2 given present value present value 600 10% 3 rate 6% 10 4 rate year 1 period 10 5 year 1 6 term $518.75-FV(H3,H5,,H2,0) future value 7 8 $636.00FV(C4,C6,,C3,0) calculation of future value 5.10(b) 9 given 200 10 present value 5.9 (b) 8% 11 given rate 600 10 12 present value year 6% period 10 13 rate 14 year $431.78-FV(H11,H13,H10,0) 2 future value 15 term 16 17 5.10(c) $674.16FVIC13,C15,,C12,0) calculation of future value 18 given future value 200 19 20 5.9 (c) 4% given rate future value 600 10 21 year 6% period 10 22 rate 1 23 year $135.11-PV(H20,H22,H19,0) 24 present value term 25 26 $566.04 PV(C22,C24 ,,C21,0) 27 5.10(d) calculation of future value given given future value 1870 future value 1870 28 8% 4% 29 rate rate 30 5.9 (d) 10 10 given year year future value 600 period 10 10 31 period 6% 32 rate 1 $866.17 present value $1,263.30 33 year present value 2 --PVH29,H31,H28,0) --PVIL29,L31.,L28,0) 34 term 5.101 presenl value is the value of any money which has the worthequal to the worth of its future value when discounted. it means that what we can buy tooday or buy in future with the money willl be equal. For example in above question it can be said that the suppose that we have 866.17 and suppose that we can buy a car with this money and interest rate is 8% then we need to have 1870 after 10 years to buy a similar car. As the interest rate decrease the present value increase. Or vice versa. For an equal given future value (5.10(d)) bigger interest rate requires lesser amount to invest whereas lower interest rate require bigger amount to invest in present 35 36 37 calculation of future value $534.00 -PV(C32,C34.C31,0) 38 39 40 1

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