Question

A house costing RM120,000 cash is purchased by making a down payment of RM40,000 and the balance is to be settled by making 120 monthly payments at 6% compounded monthly. (a) Find this monthly payment. (b) If the buyer intends to settle all of the loan by making a single payment immediately after seven years, find this single payment.

Answer 1

Solution

Cost of House-120000

Downpayment-40000

Loan amount=Cost of House-Downpayment

=120000-40000=80000

Present value of annuity=Annuity amount*((1-(1/(1+r)^n))/r)

Where r=rate of intrest per period=6%/12=.5%

n=number of compounding periods=120

Present value of anuity= Loan amount=80000

a. 80000=Annuity amount*((1-(1/(1+.005)^120))/.005)

Solving we get

Annuity amount=888.164016 (Monthly payment)

b. Now

He makes payment till end of 7 years therefore using the Present value of annuity formula,we can find out present value of payments made till end of 7 years

In this case n=number of periods=7*12=84

i =intrest rate per period=6/12=.5%

Annuity amount=888.164016

PV of annuity payment made till end of 7 years=888.164016*((1-(1/(1+.005)^84))/.005)

=60797.5291

Balance present value of loan=Loan amount-PV of annuity payment made till 7 years

Balance present value of loan=80000-60797.5291

=19202.4709

Now

Present value=Cashflow/(1+i)^m

Therefore Here

i=rate of intrest per period=6%/12=.5%

m=number of periods=12*7=84

Present value=19202.4709

Cashflow=Lump sum to be paid at end of 7 years

Puttting value in formula

19202.4709=Cashflow/(1+.005)^84

Solving we get Cashflow=29194.854=Payment to be made at end of 7 years

If you are satisfied with the answer,please give a thumbs up