Answer:
C)
log(117.50 / (117.50 - 2050(0.012) ) / log(1+0.012 )
Step-by-step 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
