Question

Sabrina took out a loan for $2050 at a 14.4% APR, compounded monthly payments of $117.50

Answer 1

C)

log(117.50 / (117.50 - 2050(0.012) ) / log(1+0.012 )

Explanation:

Formula to calculate compounded monthly payments

A = R( (1-(1+r)^-n) / r)

where

r = 0.14/12

= 0.012

A = 2050

R = 117.50

n =no. of payments

2050 = 117.50 (1 - (1 + 0.012)^-n / 0.012)

cross multiplication

2050 (0.012) / 117.50 = 1 - (1 + 0.012)^-n

1 on other side

(2050 (0.012) / 117.50) - 1 = - (1+0.012)^-n

eliminating minus sign

1 - (2050 (0.012) / 117.50) = (1+0.012)^-n

LCM

(117.50 - 2050(0.012) ) / 117.50 = (1 + 0.012)^-n

power in negative

(117.50 - 2050(0.012) ) / 117.50 = 1 / (1+0.012)^n

reciprocal

117.50 / (117.50 - 2050(0.012) ) = (1+0.012)^n

taking log

log(117.50 / (117.50 - 2050(0.012) ) = log(1+0.012)^n

Answer

log(117.50 / (117.50 - 2050(0.012) ) = n log(1+0.0120)

log(117.50 / (117.50 - 2050(0.012) ) / log(1+0.012 ) = n