Chatterton Company has obtained a $75,000 short-term loan from the bank with the
ID: 2766409 • Letter: C
Question
Chatterton Company has obtained a $75,000 short-term loan from the bank with the understanding that Chatterton will repay the loan in two equal monthly installments of $38,250 each. The first installment is due after 30 days, and the second after 60 days. Find the cost of this loan for Chatterton. Assuming 365 Days in year Cost of this loan for Chatterton per 30 days = rate(2,38250,-75000,0
) Cost of this loan for Chatterton per 30 days = 1.33% I calculated this using excel, how do you do it by hand.
Annual Cost of this loan for Chatterton = (1+1.33%)^(365/30) - 1 Annual Cost of this loan for Chatterton = 17.44% Answer Cost of this loan for Chatterton = 17.44%
Cost of this loan for Chatterton per 30 days = 1.33% I calculated this using excel, how do you do it by hand?
Explanation / Answer
Amount of Short term loan = 75000
Payment schedule = 2 equal monthly instalments
Amount of each instalment = 38250
First instalment is due after 30 days and second after 60 days
The calculation is as follows
= 2*38250 – 37500 * (1+r)^(60/365) – 37500 * (1+r)^(30/365)
76500 =37500 * (1+r)^0.16438356 + 37500 * (1+r)^0.08219178
76500 -37500 * (1+r)^0.16438356 - 37500 * (1+r)^0.08219178 = 0
At r =1% per month LHS will be
= 76500 - 37500 * (1+0.01)^1.01388888898*2 - 37500 * (1+0.01)^1.0138888889
= 76500 – 37500 * 1.02038199265 – 37500 * 1.0103959067545
= 76500 - 38205.1493 - 37850.9325
= 76500 - 76056.0818
=443.9182
At r = 2% per month or 24% per annum, LHS will be
= 76500 - 37500 * (1+0.24)^0.16438356 - 37500 * (1+0.24)^0.08219178
= 76500 - 37500 * 1.0359934 - 37500 *1.01783761
= 76500 - 38849.7525 - 38168.910375
= -518.6629
By approximation
r = 0.12 + (443.9182 * (0.12-0.24) / -518.6629-443.9182
r = 0.12 + 443.9182*-0.12/-962.5811
r = 0.12+0.05534
r = 0.17534 = 17.534% per annum
(1+r)^(30/365)*12 = 1.17534
(1+r)^0.9863013 = 1.17534
(1+r) = 1.17534^(1/0.9863013) = 1.01388896
Effective rate = 1.01388896 – 1 = 0.013888896 or 1.39% per month
The difference comes on account of rounding off of numbers after decimal after the ones shown in the working.