# Personal Bank Loan: How much must John pay the bank if he returns the loan in full in 6 months

#### nycfunction

##### Banned
John took out a loan for 3000 dollars. The bank made a payment plan of 60 months at 73.80 for 59 months and then 73.40 for the final month. The cost of his credit as a yearly rate is 15.99 percent. After 60 months (5 years), John will owe the bank a total of 4,427 dollars and 59 cents. If John pays the loan in less than 5 years, the amount he must pay the bank will NOT be 4,427 dollars and 59 cents.

A. How much must John pay the bank if he returns the loan in full in 6 months?

B. Same as A for 1 year.

C. Is there a formula to work out parts A and B? If so, what is that formula?

Thank you.

#### Wilmer

##### In Memoriam
John took out a loan for 3000 dollars. The bank made a payment plan of 60 months at 73.80 for 59 months and then 73.40 for the final month. The cost of his credit as a yearly rate is 15.99 percent. After 60 months (5 years), John will owe the bank a total of 4,427 dollars and 59 cents. If John pays the loan in less than 5 years, the amount he must pay the bank will NOT be 4,427 dollars and 59 cents.
A. How much must John pay the bank if he returns the loan in full in 6 months?
B. Same as A for 1 year.
C. Is there a formula to work out parts A and B? If so, what is that formula?
Sorry, but that problem as stated does not make sense.
Important is the rate: is it 15.99 annual effective, or .1599/12 monthly.

#### nycfunction

##### Banned
Sorry, but that problem as stated does not make sense.
Important is the rate: is it 15.99 annual effective, or .1599/12 monthly.
Sorry but the words are not my own. I found this problem online but cannot remember the site.

#### Wilmer

##### In Memoriam
Well, whoever "arranged" the problem simply didn't know what he/she was doing...

IF the payment is 73.80 and the rate is 15.99% annual cpd. monthly,
then what is owing after 6 months is THE ACTUAL BALANCE OWING AFTER 6 PAYMENTS:
Code:
  MONTH    PAYMENT    INTEREST    BALANCE
0                             3000.00
1       -73.80       39.97    2966.17
2       -73.80       39.53    2931.90
3       -73.80       39.06    2897.16
4       -73.80       38.61    2861.97
5       -73.80       38.14    2826.31
6       -73.80       37.66    2790.17
IF anything else is given as answer, then the interest rate is treated
slightly differently (perhaps simple interest)....

#### nycfunction

##### Banned
Well, whoever "arranged" the problem simply didn't know what he/she was doing...

IF the payment is 73.80 and the rate is 15.99% annual cpd. monthly,
then what is owing after 6 months is THE ACTUAL BALANCE OWING AFTER 6 PAYMENTS:
Code:
  MONTH    PAYMENT    INTEREST    BALANCE
0                             3000.00
1       -73.80       39.97    2966.17
2       -73.80       39.53    2931.90
3       -73.80       39.06    2897.16
4       -73.80       38.61    2861.97
5       -73.80       38.14    2826.31
6       -73.80       37.66    2790.17