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Author: Julia Burnside
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Compute Environment: Ubuntu 20.04 (Default)
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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.

In [1]:
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