James Hunt’s Dream Apartment
Part 1
Annual before tax income = $ 100,000
Tax rate = 25%
Monthly post tax income = 100,000 x (1 - 25%) / 12 = $ 6,250
Mother's advice: Do not spend more than 1/3 of your monthly disposable take-home pay
on housing costs (mortgage and all other housing-related expenses);
housing related expenses = $ 500 / month
disposable income available for monthly installments = 1/3 x 6,250 - 500 = $ 1,583.33
Loan period 30 years = 12 x 30 = 360
Interest rate per period = 4.75% / 12 = 0.396% per month
PV (rate, period, amount) = PV (0.396%, 360, -1583.33) = $ 303,454.85
Mother's advice 2: Always keep a minimum of $50,000 available at all times in your
savings account, in case of an emergency.
saving in savings account = $ 150,000
Savings available for payment= 150,000 - 50,000 = $ 100,000
the maximum price that James can afford to pay for the apartment
$ 303,454.85 + $ 100,000 = $ 403,454.85
Part 2
Monthly disposable income = Gross yearly disposable income / 12 x (1 - tax rate) =
125,000 / 12 x (1 - 30%) = 7,291.67
money available with him for monthly installment = 1 / 3 x monthly Disposable income other housing related expenses = 1/3 x 7,291.67 - 600 = 1,830.56
Period 15 years = 12 x 15 = 180 months
Interest rate per period = 3.50% / 12 = 0.292%
maximum loan that he can avail
PV (rate, period, amount) = PV (0.292%, 180, -1830.56) = $ 255,994.1
How much of the existing loan principal would he have to repay upfront before setting
up the new loan? (Include the closing costs to the amount).
Current outstanding loan = $ 283,333
Closing costs = $ 5,000
the amount of principal he needs to pay = $ 283,333 + $ 5,000 - $ 255994.1 = $ 32,338.9
What is the total amount of interest that he would save over the entire duration of
the loan if he were to refinance it (i.e., switch to the 15-year mortgage loan
mentioned above)?
PV =283,333
Interest rate per period = 4 % / 12 = 0.3333%
Period to maturity = 30 - 4 = 26 years = 12 x 26 months = 312 months
total interest that will be paid over the tenure of the loan = CUMIPMT (Rate, period, PV,
Start period, End period, type) = CUMIPMT (0.3333%, 312, 283333, 1,312, 0) = $172834
If he replaces the old loan by a new one,
PV of the loan amount = $ 255,994.1
Interest rate per period = 3.50% / 12 = 0.292%
Period to maturity = 15 years = 12 x 15 months = 180 months
total interest that will be paid over the tenure of the loan = CUMIPMT (Rate, period, PV,
Start period, End period, type) = CUMIPMT (0.292%, 180, 255994.1, 1,180, 0) =
$ 73,506.7
interest saved = 172834 - 73,506.7 = 99327.48
Can he afford to refinance his loan, all things considered? Should he do it? Explain.
In order to refinance, he needs to repay an amount of $ 32,338.9 upfront.
Money in his savings account = $ 80,000
balance he needs to maintain = $ 50,000
money available for immediate payment = $ 80,000 - $ 50,000 = $ 30,000 < $ 32,338.9 =
amount that required upfront
He will not be able to refinance his loan.
Yes, he should refinance the loan as there is a significant interest cost savings for him.
Felix’s Retirement Plan
a) What will be the $ value (to the nearest cent) of
the investment in bonds at maturity, i.e., 20 years
from today, after the fees are paid and assuming
that the bonds perform as predicted?
Management fee = 5%*1000 = 50 (per month)
Monthly investment = 1000-50= 950
So, 950/2 = 475
475$ will be in bond and 475$ will be in stocks
Rate= 4%/12 = 0.003333%
Period = 20 * 12 = 240
Pmt= 475
Fv(rate,period,pmt) = 174,210,12
b)What will be the $ value (to the nearest cent) of
the investment in stocks at maturity, i.e., 20 years
from today, after the fees are paid and assuming
that the stocks perform as predicted?
Management fee = 5%*1000 = 50 (per month)
Monthly investment = 1000-50= 950
So 950/2 = 475
475$ will be in bond and 475$ will be in stocks
Rate= 8%/12 = 0.006667
Period = 20 * 12 = 240
Pmt= 475
Fv(rate,period,pmt) = 281,179.55
c)What will be the true rate of return on the entire
investment plan, expressed as an Effective Annual
Rate (EAR), assuming that bonds and stocks
perform as predicted? (the EAR should contain 4
decimals)
Total return= return on bonds + return on stocks
= 0.04*0.5+ 0.08*0.5
=0.06
Nominal rate of return= 0.06
Period =12
Effect annual rate(effect(nominal_rate,npery) = 6.1678%