You took a loan of 500000 AED to buy an apartment at 12 per

You took a loan of 500,000 AED to buy an apartment at 12% per year compounded monthly over 5 years. Knowing that the represent the market interest rate. If the average monthly inflation rate is 0.25% What\'s the nominal inflation rate per year Determine the monthly real interest rate and the nominal annual real rate Compute the monthly payment in constant dollars.

Solution

Loan=500000 AED

Nominal interest rate=12% per year

Average monthly infation rate=0.25%

A.) nominal inflation rate per year=0.25(12)=3%

B.) Nominal interest rate per year= 12%

nominal interest rate per month=12/12%=1%

inflation rate per month=0.25%(given)

Monthly Real interest rate= monthly nominal interest rate-monthly inflation rate

                                     = 1-0.25=0.75%

It should be Annual real rate instead of nominal annual real rate

Annual real rate=Annual nominal interest rate- infation rate annual

                       =12-3=9%

c.)Monthly payment=Loan amount[monthly interst rate]^12(1/12)

formula is= loan[interst rate monthly]^{no of months multiplied by time for which amount is calculated that is one month}

and one month =1/12 year

Monthly payment=500000[1/100]^12(1/12)

                         =500000(0.01)=5000 AED

1 AED=0.27 USD

5000 AED=5000(0.27 )USD=1350 USD