question archive You would like to have $250,000 in 10 years to be used as a down payment to buy a house
You would like to have $250,000 in 10 years to be used as a down payment to buy a house
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You would like to have $250,000 in 10 years to be used as a down payment to buy a house. You therefore plan to deposit each month an equal sum of money into your bank? account, with the bank paying 8?% per? annum, compounded monthly.
(a) If these deposit amounts will be made at the beginning of each? month, how much must you deposit monthly to accumulate ?$250,000??
(b) ?Alternatively, you decide to make one large lump sum deposit today instead of monthly? deposits, how much should this lump sum deposit? be? (assuming the interest rate 8?%.a. compounded? monthly)
(c) Assume it is now the end of Year 10? (i.e. today), you decide to take up a 25?-year fully amortized loan with an annual percentage rate of 6.6?% and the repayments are made at the end of each month. If the purchase price of the house is? $1,000,000 and you use the accumulated ?$250,000 as a? deposit, what would the monthly repayments? be?
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a) We can calculate the monthly deposit by using the following formula in excel:-
=pmt(rate,nper,pv,-fv,type)
Here,
Pmt = Monthly deposit
Rate = 8%/12 = 0.6667% (monthly)
Nper = 10*12 = 120 periods (monthly)
PV = $0
FV = $250,000
Type = 1
Substituting the values in formula:
= pmt(0.6667%,120,0,-250000,1)
= $1,357.47
b) Computation of Lump sum Deposit using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Lump sum Deposit = ?
Rate = 8%/12 = 0.6667% compounded monthly
Nper = 10 years * 12 months = 120 months
PMT = 0
FV = $250,000
Substituting the values in formula:
=-pv(0.6667%,120,0,250000)
PV or Lump Sum Deposit = $112,626.39
c) We can calculate the monthly repayments by using the following formula in excel:-
=pmt(rate,nper,pv,-fv,type)
Here,
Pmt = Monthly Repayments = ?
Rate = 6.6%/12 = 0.55% (monthly)
Nper = 25*12 = 300 periods (monthly)
PV = $1,000,000-$250,000 = $750,000
FV = 0
Type = 0
Substituting the values in formula:
= pmt(0.55%,300,-750000,0,0)
= $5,111.02
