Suppose you borrow $12,000 to buy a car. The loan is to be paid in 60 equal mont

Question

Suppose you borrow $12,000 to buy a car. The loan is to be paid in 60 equal monthly installments at an interest rate of 5% per year.

   Assume that the payments are actually made continuously at whatever rate is needed to pay off the loan in 60 months. Determine the continuous rater per month that would be required. (Hint: The problem is easier if you think about it from the lender's point of view. The amount owed begins at $12,000. It increases continuously by a natural growth process and decreases continuously at a fixed rate. In 5 year the amount owed is zero.)

Explanation / Answer

Fixed payment loan. Example: car loan, student loan or mortgage with monthly payments. Payments are part interest, part principal. Fully amortized loans, so that the balance at maturity is 0. Formula for calculating the payment on this type of loan.

PMT= PV*i/(1- 1/(1+i)^n)

PV = loan amount in dollars
n = number of payments (periods)
i = interest rate per period.

here,

PV=$12000

i=5/12 =0.4167%

n=60

==> PMT= 12000*0.4167*10^-2/(1-1/(1.004167)^60) =$64.19

the continuous rater per month that would be required =$64.19

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