a)Qiqi has overused her credit card. She decides to only pay cash until the bala

Question

a)Qiqi has overused her credit card. She decides to only pay cash until the balance of $8,574 is paid off. The credit people charge 18% compounded monthly.

How much interest will she owe on the first month's payment?

b)The Bowmanville Town Council has decided that the dam just upstream of the town must be rebuilt and strengthened. The town engineer estimates that it will cost $85,000 by the end of the year. Subsequent annual repair costs will decline by $10,000 per year, making the second year cost $75,000, the third, $65,000 and so on. Council members want to know the equivalent present cost of the repairs for the next 5 years, at 4%. You respond "to the nearest dollar, it will be..."

c)You are setting up your pension fund. You have found an amazing fund that pays 14% compounded continuously. If you deposit $1,200 a month for 7 years, what will be your balance at the end of the seven-year period?

d)A set of cash flows begins at $50,000 and increases at 10% per annum for the next 15 years. If the interest rate is 7%, what is the present value of the set (to the nearest dollar)?

Explanation / Answer

a)interest she owe on the first month's payment=

=8574*18%/12 ( As yearly rate =18% but compounded monthly, so after moth rate =18%/12)

=$128.61

b)=> present value=85000/(1.04) +75000/(1.04)^2 +65000/(1.04)^3 +55000/(1.04)^4 +45000/(1.04)^5

=$292,858.2

Estimated value of cost for The Bowmanville Town Council = $292,858.2

c)balance at the end of the seven-year period=

=1200*e^(0.14*7) (As continous compounding, Fv =PV*e^rt)

=$3197.34

d)present value of the set =50000*(1-(1.1/1.07)^15)/(0.1-0.07)

=$992,383

e) After year 1 value = 5000*(1.08) = $5400 ,amount paid =500 , so remaing amount after 1 year= 5400-500=$4900

After year 2, value =4900*(1.08) =$5292, amount paid =1000, amount remaining = $4292

After year 3,value =4292*(1.08) =$4635.36,amount paid =1000,amount remaining = $3635.36

After year 4 , value =3635.36*1.08 =$3926.19,amount paid =2000, amount remaining at end of 4th year = $1926.19

At end of 5th year there is no remaining balnce so amount paid in year 5 ,(X) =$1926.19

=> X=$1926.19

f) equation that describes cash flow is

present value =-100+50/(1+r) +60/(1+r)^2 +70/(1+r)^3 +80/(1+r)^4 +140/(1+r)^5

g)effective interest rate =(1+r/12)^12 -1

=(1+18/1200)^12 -1

=19.56%

h)=> 8574 = 225*(1+18/1200)^n ( As 18% per year., per month =

=> n=ln(38.1)/ln(1.015)

=> n=244.5 months

so it will take 244 and half months

i) present value =400/(1.05) +500/(1.05)^2+600/(1.05)^3+700/(1.05)^4+800/(1.05)^5 +900/(1.05)^6 +1000/(1.05)^7 (As n=7 yrs)

=$3937.75

So we have to set aside $3937.75 for maintainance

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