Question

s.) 3. A person buys a car for $5500.00 and makes monthly payments of $200.00 for 36 months. Assuming a monthly compounding period, compute the nominal and effective interest rates per year for this transaction. Draw Cash flow diagram and show standard notation equation.

Answer 1

Nominal interest rate:
Nominal interest during the whole loan tenure = Gross sum repaid in 36 months - Original loan amount
Nominal interest during the whole loan tenure = ($200*36) - $5500
Nominal interest during the whole loan tenure = $1700
Yearly average of interest paid = $1700 / 3 = $566.67
Nominal interest rate = $566.67 / $5500 * 100
Nominal interest rate = 10.30% p.a.


Effective interest rate:
Let effective interest rate be = r
Now our equation will be:

$5500 = $200*(1 / 1+r/12)¹ +  $200*(1 / 1+r/12)² + $200*(1 / 1+r/12)³ + $200*(1 / 1+r/12)⁴ + .....so on till....... + $200*(1 / 1+r/12)³⁶

When we solve it, we will find that r comes out to be 18.42% p.a.
Effective Interest rate = 18.42% p.a.

It's cash flow diagram can be as below:



Standard notation equation:

P = M/(1+r/12)^t1 + M/(1+r/12)^t2 + M/(1+r/12)^t3 + M/(1+r/12)^t4 + ..... as so on till........M/(1+r/12)^tn

Where:
P = Principal amount
M = Monthly payment
r = Effective interest rate
t = Monthly payment number from 1 to 36 as per the given question).