13. I have made a careful assessment of my financial needs on retirement, in exa
ID: 2648144 • Letter: 1
Question
13. I have made a careful assessment of my financial needs on retirement, in exactly 30 years time. Taking into account inflation, and my future living expenses on retirement, I calculate that I will need a nest-egg of $1,200,000. I have found a savings scheme which promises a return of 6% per annum, compounded annually. How much (to the nearest cent) will I need to save at the beginning of each year (first instalment starts right now) if I am to accumulate my nest-egg after thirty years?
14. I want to buy a new car, as my old one has just failed its annual inspection. Right now I can only afford to pay $250 per month, but in two years time I should be able to pay $400 per month. A local finance company quoting rates of 12% per annum, compounded monthly, has offered to extend me a five-year loan whereby I pay them $250 at the end of each month for the next two years, and $400 per month for the three years after that. How expensive a car can I afford to buy (to the nearest dollar)?
15. Today is June 1st and I have just deposited $5,000 in a bank account paying a fixed 5% per annum interest rate over the next six months, calculated according to the Actual/360 convention. How much (to the nearest cent) will I be able to withdraw on December 1st?
13. I have made a careful assessment of my financial needs on retirement, in exactly 30 years time. Taking into account inflation, and my future living expenses on retirement, I calculate that I will need a nest-egg of $1,200,000. I have found a savings scheme which promises a return of 6% per annum, compounded annually. How much (to the nearest cent) will I need to save at the beginning of each year (first instalment starts right now) if I am to accumulate my nest-egg after thirty years?
14. I want to buy a new car, as my old one has just failed its annual inspection. Right now I can only afford to pay $250 per month, but in two years time I should be able to pay $400 per month. A local finance company quoting rates of 12% per annum, compounded monthly, has offered to extend me a five-year loan whereby I pay them $250 at the end of each month for the next two years, and $400 per month for the three years after that. How expensive a car can I afford to buy (to the nearest dollar)?
15. Today is June 1st and I have just deposited $5,000 in a bank account paying a fixed 5% per annum interest rate over the next six months, calculated according to the Actual/360 convention. How much (to the nearest cent) will I be able to withdraw on December 1st?
Explanation / Answer
13. Using excel formula, annual savings = PMT(6%,30,0,-1200000,1) = $14,319.52
where rate = 6% per annum
nper = 30 years
pv = 0
fv = -1200000
type = 1 (beginning of period)
14. The total present value of the loan = PV(monthly installment of $250 per month for 2 years) + PV(monthly installment of $400 for 3 years)/factor(1% per month for 24 months)
PV(monthly installment of $250 per month for 2 years) = PV(12%/12,24,-250,,0) = $5310.85
Where rate = 12%/12 per month
nper = 24 months
pmt = -250
type = 0 (end of period)
PV(monthly installment of $400 for 3 years)/factor(1% per month for 24 months)
= PV(12%/12,36,-400,,0)/(1.01^24) = 9484.66
Total = 5310.85+ 9484.66 = 14,795.51 ~ $14,796
15. Dec 1 - Jun 1 = 183 days
Amount on 1st dec = 5000 + 5000*0.05*183/360 = 5000 + 127.08 = $5,127.08
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