Problem 193503 · hard · Phase 01 Prerequisites & Setup

How Long Until the Loan Is Gone?

input · while loops · arithmetic · rounding · f-strings · conditionals

A borrower pays the same amount every month. Read three lines: the amount borrowed, the yearly interest rate in percent and the monthly payment. Amounts have 0-2 decimals and may use comma thousands separators (12,500.5); the rate has 0-3 decimals.

Each month, in this order:

  1. interest = balance × rate / 100 / 12, rounded to the nearest cent, halves up; add it to the balance;
  2. if the balance is now at most the payment, the borrower pays exactly the balance and the loan is finished; otherwise the payment is subtracted and the next month starts.

If the loan finishes, print:

Payments: <number of payments>
Last payment: <money>
Total interest: <money>
Duration: <duration>

Money is $ + dollars with comma separators + . + two-digit cents. The duration uses years of 12 months: <Y> year(s) <M> month(s), with year/month in the singular for 1, and a part left out when it is 0 (1 year, 2 years 1 month, 7 months).

If the loan can never finish (the interest is at least the payment while the balance is still larger than the payment), print only Never paid off.

Examples

Input:
1,000
12
300
Output:
Payments: 4
Last payment: $122.48
Total interest: $22.48
Duration: 4 months

Input:
10000
6
50
Output:
Never paid off

Constraints

  • borrowed amount between 0.01 and 9,999,999.99; rate between 0 and 40
  • payment at least 0.01; a loan that finishes needs at most 3000 payments

Goals

  • Simulate month-by-month interest with rounding to the cent at every step
  • Detect a payment that can never finish the loan
  • Print durations with correct singular and plural words
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