Interest Rate.ipynb

Kernel: Python 3 (system-wide)

Determining the Interest Rate

Rent-A-Center advertises an Amana refrigerator for $$95.30$ per month.

The actual cost of the refrigerator is $$787.50$.

The advertised payment plan cost is $$1810.70$ (disregarding taxes and promotional offer).

The annual interest rate is $122.22\%.$

You would be paying $$1023.20$ in interest.

Alternatively, it would take $9$ month of saving $$95.30$ per month in order to afford the refrigerator at the original price of $$787.50.$

import math


r=1+((((95.3*19)/787.5)-1)/12)

def newton(c, d, r, n, err):
    i=0
    while abs(c(r)) > err and i <=n:
        r=r-c(r)/d(r)
        i+=1
        print(r)
    if i > n:
        return False
    else:
        return r
    
def rate(r):
    return 787.5*r**(19+1) - (787.5+95.3)*r**19 + 95.3

def rate_deriv(r):
    return 787.5*(19+1)*r**19 - (787.5+95.3)*19*r**(19-1)


print('\nAnnual interest rate: ', round(12*(newton(rate, rate_deriv, r, 4, 0.0001)-1)*100, 2), '% \n')
print('Actual cost of refrigerator: $787.50 \n')
print('Price paid after 19 monthly payments of $95.30: $', 19*95.3, '\n')
print('Total interest paid: $', (19*95.3)-787.5, '\n')
print('Time it would take to save $95.30 per month in order to afford the refrigerator: ', math.ceil(787.5/95.3), 'months \n')

1.1026197834115743
1.1018634692604634
1.1018508808927683

Annual interest rate:  122.22 % 

Actual cost of refrigerator: $787.50 

Price paid after 19 monthly payments of $95.30: $ 1810.7 

Total interest paid: $ 1023.2 

Time it would take to save $95.30 per month in order to afford the refrigerator:  9 months