# How can I calculate minimum payment on quick loan? [closed]

I am working on calculator for quick loans. Client can select how much he will pay monthly. Base on it payment schedule will be calculated. Payment interest depends on 1 payment period. Number of payments is limited. How can I calculate what is a minimum monthly payment if I know that number of payments should be 5, amount of loan is 250, APR is 70% and payment periods are next:

• 1 payment - 9 days,
• 2 payment - 30 days
• 3 payment - 28 days
• 4 payment - 30 days
• 5 payment - 32 days

Is it possible to calculate minimum based on this logic?

• This question appears to be off-topic because it is about software development – Dheer Jun 20 '14 at 9:57

APR is 70%, compounded monthly (assumed). First convert to effective annual rate

``````ear = (1 + 0.7/12)^12 - 1 = 0.9746 = 97.46 %
``````

The term of the loan is 129 days, so the interest rate for the term is

``````i = (1 + ear)^(129/365) - 1 = 0.2718 = 27.18 %
``````

The log rate is

``````r = ln(1 + i) = 0.2405
``````

Without any repayments the amount owed at the end of the loan term would be

``````250 e^r = 317.955
``````

which can also be calculated from

``````250 (1 + i) = 317.955
``````

For equal payments

``````-250 e^r + p e^((120/129)r) + p e^((90/129)r) + p e^((62/129)r) + p e^((32/129)r) + p = 0
``````

therefore `-317.955 + 5.61728 p = 0`

therefore `p = 56.6031`

giving a total cost of loan of `5 * 56.6031 = 283.015`

However, if the payments do not have to be equal, the cost of the loan can be minimised by paying it all off in the first installment

``````-250 e^r + p e^((120/129)r) = 0
``````

giving a single repayment on day 9 of `p = 254.229`

Check

The daily rate is

``````d = (1 + ear)^(1/365) - 1 = 0.0018657 = 0.18657 %
``````

Cost of loan paid off after 9 days is `250 (1 + d)^9 = 254.229`