Hello, aznmartinjai!

A strange problem ... I hope I interpreted it correctly.

. . . . . . . . . . . . . . . . . . . . . . . i(1 + i)^nTwo banks are offering car loans. .You wish to borrow $5000.

The fixed payments for each loan are $100 per month.

Bank A changes 1 percent interest per month on the unpaid balance.

Bank B charges 1.5 percent per month on the unpaid balance

and will throw in a television set valued at $1000.

If you could use the TV set, which loan would you pick?

Amortization Formula: . A .= .P ---------------

. . . . . . . . . . . . . . . . . . . . . . (1 + i)^n - 1

where: P = amount of loan

. . . . . .i = perioidic interest rate

. . . . . n = number of periods

. . . . . A = periodic payment

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Bank A: .P = 5000, i = 0.01, A = 100

. . . . . . . . . . . . . . . . . .0.01(1.01)^n

We have: . 100 .= .5000 ----------------

. . . . . . . . . . . . . . . . . . (1.01)^n - 1

Then we have: . (1.01)^n - 1 .= .½(1.01)^n

. . . . . . . . . . . . . ½(1.01)^n .= .1

. . . . . . . . . . . . . . (1.01)^n .= .2

Take logs: . . . . . .n·ln(1.01) .= .ln(2)

. . . . . . . . . . . . . . . . . . . . . . . . ln(2)

. . . . . . . . . . . . . . . . . . . n .= .--------- .= .69.6607...

. . . . . . . . . . . . . . . . . . . . . . . ln(1.01)

You will be paying $100 per month for 70 months

. . a total of $7,000.

You will pay $2,000 in interest charges.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Bank B: .P = 5000, i = 0.015, A = 100

. . . . . . . . . . . . . . . . . .0.015(1.015)^n

We have: . 100 .= .5000 -------------------

. . . . . . . . . . . . . . . . . . (1.015)^n - 1

Then we have: . (1.015)^n - 1 .= .¾(1.015)^n

. . . . . . . . . . . . . ¼(1.015)^n .= .1

. . . . . . . . . . . . . . (1.015)^n .= .4

Take logs: . . . . . .n·ln(1.015) .= .ln(4)

. . . . . . . . . . . . . . . . . . . . . . . . . ln(4)

. . . . . . . . . . . . . . . . . . . . n .= .----------- .= .93.11105...

. . . . . . . . . . . . . . . . . . . . . . . . ln(1.015)

You will be paying $100 per month for 93 months

. . a total of $9,300.

You will pay $4,300 in interest charges.

Even with the $1000 TV set, you will play more than at Bank A.

Take the loan from Bank A.