You purchase a house today for $250,000. You pay a 10% deposit and borrow the re

Question

You purchase a house today for $250,000. You pay a 10% deposit and borrow the

remainder.

(a) If repayments for the borrowing are made each month over the next 20 years,

what will be the monthly repayment assuming an interest rate of 6% p.a.

(b)If you pay off $2,000 per month, how long will it take to repay the loan?

You bought a car for $5,000 and sold it two months later for $5,200.

(a) What is the simple annual interest rate implicit in this transaction?

(b) What is the corresponding effective annual interest rate?

(c) If inflation is running at 3% pa, what is the real effective annual interest rate?

Explanation / Answer

You purchase a house today for $250,000. You pay a 10% deposit and borrow the remainder.

(a) If repayments for the borrowing are made each month over the next 20 years, what will be the monthly repayment assuming an interest rate of 6% p.a.

Loan amount = 90%*250,000 = 225,000 = PV

No of periods = 20Yr*12 mon/Yr = 240

Rate = 6%/12

So Monthly payment = PMT(rate,nper,pv,fv)

= PMT(6%/12,240,225000,0)

= $1612

(b)If you pay off $2,000 per month, how long will it take to repay the loan?

SO PV = 225000, PMT = 2000, Rate =6%/12

So No of months to repay = nper(rate,pmt,pv,fv)

= nper(6%/12,2000,225000,0)

= 89 months

You bought a car for $5,000 and sold it two months later for $5,200.

(a) What is the simple annual interest rate implicit in this transaction?

Interest for 2 months = 5200-5000 = 200

So Annual Int = 200*12/2 = 1200

Pricipal = 5000

So Int rate = 1200/5000 = 24%

(b) What is the corresponding effective annual interest rate?

EAR = (1+ i/n)^n -1 = (1+24%/12)^12 - 1 = 26.82%

(c) If inflation is running at 3% pa, what is the real effective annual interest rate?

Real EAR = (1+(24%+3%)/12)^12 - 1 =30.60%

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