Contact Us!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.

| Download
Views: 186
Image: ubuntu2004
Tweet
Share
Share
Kernel: Python 3 (system-wide)

Determining the Interest Rate

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

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

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

The annual interest rate is 122.22%.122.22\%.

You would be paying $1023.20$1023.20 in interest.

Alternatively, it would take 99 month of saving $95.30$95.30 per month in order to afford the refrigerator at the original price of $787.50.$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