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decision: She can buy a computer for $1,000 and pay $10 per month for Intenmet access for three years, or she can A consumer faces the receive a $450 rebate on the computer (so that its cost is $550) but agree to pay $25 per month for three years for Internet access. For simplification, assume that the consumer pays the access fees yeany (e $10 per month $120 per year, at the beginning of each yearn) What should the consumer do if the interest rate is 6 percent? If the interest rate is 6 percent, then the consumer should take What if the interest rate is 12 percent? If the interest rate is 12 percent, then the consumer should not take the rebate At what interest rate would the consumer be indifferent between the two options? The consumer would be indifferent i the interest rate werepercent(Enter a numeric response rounded to two decimal places) Enter your answer in the answer box

Solution

In first option he pays $1000 at the begining and then$10 per month ie $120 per year for 3 years

Present Worth of IWithout rebate Nvestment=$1000+$120/1.06+$120/1.06^2+$120/1.06^3=$1320.76

Present Worth of IWith rebate Nvestment=$550+$300/1.06+$300/1.06^2+$300/1.06^3=$1351.9

Hence when Interest rate is 6% he should go without rebate...

ANs b)

When Interest rate is 12%

Present Worth of IWithout rebate Nvestment=$1000+$120/1.12+$120/1.12^2+$120/1.12^3=$1288.21

Present Worth of IWith rebate Nvestment=$550+$300/1.12+$300/1.12^2+$300/1.12^3=$1270

Hence in this case he should choose an option of with rebate because cosr is lower in this case

Now lets assume interest rate to be x where consumer is indifferent

ie

PW for costs are same

$1000+$120/1+x+$120/(1+x)^2+$120/(1+x)^3=$550+$300/(1+x)+$300/(1+x)^2+$300/(1+x)^3

450=180/(1+x)+180/(1+x)^2+180/(1+x)^3

2.5=1/(1+x)+1/(1+x)^2+1/(1+x)^3

then x=9.95% using trial and error