Question

8. You purchased a new car for sis,000. The dealer offers you an interest rate of 5% over years. a) What would your monthly payment be? b) Suppose you would like to save interest by paying the loan off in 3 years. How much more a ma would you need to pay? c) What would the effective interest rate be if you paid off the car in 3 years? 9. Sketch the annual cash flow diagrams for each case in Question 8

Answer 1

8)

a)

Using the PMT formula in excel, which returns the periodic payment for a loan, the amount to be paid monthly for 5 years with an interest rate of 5% is $283.07 .

(In the formula you divide the interest rate by 12 because that rate if for the entire year and in order to get the monthly rate you divide it by 12.

Number of periods you are paying is 12*5 because the loan is paid back monthly and hence you will be making 60 payments through the 5 years to pay back the loan)

LOAN	15000
Interest	5%
Period	5
No. of Payments	60	(5*12)
Monthly Payment	$283.07	PMT(5%/12,60,15000)

b)  If the pay-back period was only 3 years then , the monthly payment will increase by $166.49.  So you will have to pay $166.49 more a month to pay the loan within 3 years

LOAN	15000
Interest	5%
Period	3
No. of Payments	36	(3*12)
Monthly Payment	$449.56	PMT(5%/12,36,15000)

EXTRA

$166.49

(449.56-283.07)

c) Effective interest rate is the that is earned on an investment or paid on a loan (in this case loan) that is a result of compounding over a specific period of time.

EFFECTIVE INTEREST RATE	0.051162
	5.11619	(1+r/n)^n-1	((1+(5%/12))^12)-1

The formula is 1+ the nominal interest rate (r) that is divided by the number of compounding periods (n) to the power n and minus 1

r = stated rate of interest rate (5%)

n= number of compounding periods ( here it is monthly so 12 )

9)

a) ) The upward arrow mean INFLOW. The downward arrow means OUTFLOW.

So, in case of 5 years pay-back period the yearly outflow will be $283.07*12 = $3,396.82

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b)

In case of 3 years pay-back period the yearly outflow will be $449.56*12 = $5394.76

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