Using a negative exponent

Question

This is the problem I'm working on

This is my code

p = int(input('Enter the amount of the loan: '))
r = float(input('Enter the interest rate: '))
d = int(input('Enter the length of loan in months: '))
if p > 0 and r > 0 and d > 0:
    m_payment = (p*r)/(1-(1+r) ** 1/d)
    t_interest = d*m_payment-p
else:
    print('Enter a postive number')
print('Monthly payment: ${0:.2f}'.format( m_payment))
print('Total interest paid: ${0:.2f}'.format(t_interest))

Am I correctly inputting the exponent?

Operator precedence doesn't care about how many spaces you use. The spaces on either side of `**` don't change its precedence. — user2357112, Mar 21 '17 at 19:41
You don't have a negative exponent. You did `1/d`, not `-d`, plus `d > 0` according to the conditional — OneCricketeer, Mar 21 '17 at 19:42
I believe what you really want is `m_payment = (p*r)/(1-1/(1+r)**d)`. — Matt Cremeens, Mar 21 '17 at 19:42
The problem is attached. Isn't a negative exponent just a number taken to the 1/n power? — Jeremy, Mar 21 '17 at 19:51
That would be the n-th root. `x ^ 1/2` like `sqrt(x)`. Not `x^-2` — OneCricketeer, Mar 21 '17 at 19:54
@Jeremy `"r is the monthly interest rate (annual rate divided by 12)"`, so the user inputs the `annual rate` and you just need to convert that to a `monthly rate`, divide `r` by `12`, i.e. `r = float(input('Enter the interest rate: '))/12.` — chickity china chinese chicken, Mar 21 '17 at 20:02
If you think a negative exponent is a number to the `1/n` power, your question is really about math and not programming. — BrenBarn, Mar 21 '17 at 20:27

score 2 · Answer 1 · answered Mar 21 '17 at 20:08

1) Formula uses n, not d, so why not use n?

Anyway...

Am I correctly inputting the exponent?

Did you get the output given as shown? You can use a normal calculator to verify those numbers.

That being said, if you read the question carefully, you are initially inputting "annual interest", not r. The instructions say that r is annual interest over 12.

So here is that adjustment to your code.

p = annual_interest = n = -1
while True:
  p = int(input('Enter the amount of the loan: '))
  annual_interest = float(input('Enter the interest rate: '))
  n = int(input('Enter the length of loan in months: '))
  if p <= 0 or annual_interest <= 0 or n <= 0:
    print('Enter a postive number')
  else:
    break

r = annual_interest / (12 * 100)  # this needs to be a decimal percentage

Then, 1/n is not a negative exponent, it is the N-th root. You can just put a negative exponent in Python, no need to try to think you can re-write it any differently.

monthly_payment = (p * r) / (1 - ((1 + r) ** -n))
interest = n * monthly_payment - p

score 0 · Answer 2 · answered Mar 21 '17 at 20:26

0

No. you are not using the exponent correctly. The formula clearly states that you have to use a negative expononent, but you are trying to get the dth-root.

answered Mar 21 '17 at 20:26

DahliaSR

77
6

chickity china chinese chicken · Answer 3 · 2017-03-21T20:36:26.260

The problem appears to only be in the handling of the "annual interest rate" as a "monthly interest rate" converted to a decimal percentage, and the exponent should remain as an integer, only negated.

Keeping your code close to as it is:

p = int(input('Enter the amount of the loan: '))
r = float(input('Enter the interest rate: '))
d = int(input('Enter the length of loan in months: '))

mr = (r/100)/12 # convert annual interest rate to a decimal monthly interest rate

if p > 0 and r > 0 and d > 0:
    m_payment = (p*mr)/(1-((1+mr) ** -d))
    t_interest = d*m_payment-p
else:
    print('Enter a postive number')
print('Monthly payment: ${0:.2f}'.format( m_payment))
print('Total interest paid: ${0:,.2f}'.format(round(t_interest))) # given answer appears rounded

demo:

Enter the amount of the loan: 18000
Enter the interest rate: 5.25
Enter the length of loan in months: 60
Monthly payment: $341.75
Total interest paid: $2,505.00

No worries, I didn't read it carefully at first either, as you can see it took me a long time to figure it out... and the purpose of that textbook-problem may have just been to solve that. It also helped us all brush up on our basic math concepts too. :) Hope it helped. — chickity china chinese chicken, Mar 21 '17 at 23:42

Using a negative exponent

3 Answers3