Question

Suppose you have selected a new car to purchase for 7,50,000 If the car can be financed over a period of 4 years at an annual rate of 6.9% compounded monthly, how much will your monthly payments be? How much of your first payment is interest?
A) 18925 and 4556
B) 17925 and 4667
C) 18756 and 3475
D) 17925 and 4313
Please explain

Answer 1

Given :-

• Price of car = 7,50,000
• Time = 4 years.
• Annual rate = 6.9% compounded monthly .

To Find :-

• Monthly payment and first payment of interest .

Solution :-

we know that,

• Amount = Principal * [ 1 + R ]^(Time in years * 12)
• R = rate / 100
• we multiply by 12 to find amount for total 48 months.

Putting all values we get,

→ R = 6.9/100 = 0.069

→ Total Amount to be paid = 750000 * [ 1 + 0.069 ]⁴⁸ = 860,395.57 .

Therefore,

→ Each monthly payment will be = ( Total amount ) / Total payments = (860,395.57 / 48) = 17924.90 ≈ 17925 .(Ans.)

Now,

→ Principal in first month = 7,50,000

→ Rate = 6.9% monthly = (6.9/12) % per annum.

So,

→ interest of first month = (Principal * Time * Rate) / 100 = (750000 * 6.9 ) / (100 * 12) = 4,312.5 ≈ 4313 (Ans.)

Hence, Option (D) is correct answer.