The topic is as follows:

A car company adopted a more flexible payment method for promotion. For a car with 65,438+10,000 yuan, under the premise of paying off all the money within one year, you can choose the following two stages to buy a car:

Option 1: Pay in three installments, the first payment four months after purchase, the second payment four months later and the third payment four months later.

Scheme 2: 12 installment payment, the first payment after purchase 1 month, the second payment 1 month, and the first 12 month after purchase.

It is stipulated that the repayment amount of each installment is the same, and the monthly interest rate is 0.8%. The monthly interest is calculated according to compound interest, which means that the interest of last month should be recorded in the principal of next month.

Comparing the above two schemes, which scheme has less total payment? Give the reasoning process.

(Reference data: 1.008 3 ≈ 1.024, 1.008 4 ≈ 1.032,1.0081≈.

Answer:

Suppose you have to pay x million yuan each time.

For scheme 1:

When the down payment (i.e. 12/3 months after the loan) is 10000 yuan, it is (12- 12/3=8) months short of the payment.

The deposit period of this X million yuan is 8 months, which is determined by the compound interest formula.

The sum of this sum and interest is: x (1+0.008) (12-12/3) = x ×1.008 8.

In the same way; In a similar way

For option 2:

When the down payment (that is, after the loan12-1=1month) is 10000 yuan, it is still far from the time of payment (12-1=/kloc-)

The deposit period of this X million yuan is 1 1 month, which is determined by the compound interest formula.

The sum of this sum and interest is: x (1+0.008) (12-1) = x ×1.0081.

Answer reference:

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Attached:

Using the knowledge of sequence, there is an installment formula: x = a (1+p) m [(1+p) m/n-1]/[(1+p) m-1].

Namely:

Correlation of installment payment