Question

      Ms. Cressida bought a car for $48,000 exactly three years ago. After making an up-front equity payment of $5,000, she borrowed the rest of the car value from her bank in the form of a five-year loan. She negotiated a loan rate of 2.5% APR with semi-annual compounding. She makes loan payments of an equal dollar amount every two weeks (i.e., biweekly), and her first loan payment was due two weeks after she signed the loan contract.                                                    (10 marks total)

1. What is the effective annual rate on Cressida’s loan?     (1 mark)
2. What is the effective biweekly interest rate on Cressida’s loan?                                                               (1 mark)
3. What is Cressida’s biweekly loan payment?                   
4. What is Cressida’s current loan balance?                      
5. What is the total amount of interest that Cressida would have paid to the bank after five years of loan payments?      

Show the amortization schedule (table) for the first five payments and the last five payments in the amortization table provided below. Round your answers in the table to two decimal places.

Answer 1

Given APR =	2.5%
Compounding -semi annual
EAR =(1+2.5%/2)^2-1 =2.52%	Ans a.
So biweekly interest rate=2.52%/24=	0.105%	Ans b.

Price of car	$        48,000
Less upfront payment	$          5,000
Loan amount	$        43,000
Formula for loan amortization =
A= [i*P*(1+i)^n]/[(1+i)^n-1]
	Amt $
A = periodical installment	?
P=Loan amount =	$        43,000
i= interest rate per period =	0.105%
n=total no of payments	120.00

A =[0.00105*43000*1.00105^120]/[1.00105^120-1]
A=381.57
So the biweekly installment =	381.57	Ans c.

Loan balance now =after 3 years

The next formula is used to calculate the remaining loan balance (B) of a fixed payment loan after p months

B = P[(1 + i)^n - (1 + i)^p]/[(1 + i)^n - 1]

p=72
B=43000*[1.00105^120-1.00105^72]/[1.00105^120-1]
B=17852.34
So Loan Balance now =	$ 17,852.34	Ans d.
Total amount payable in 120 installments =120*381.57=	$        45,788
Less Loan amount	$        43,000
Total Interest payable on Loan	$     2,788.40	Ans e

Period	Opening Loan Balance	Monthly Installment	Interest paid	Principal repaymnet	Outstanding principal
1.00	$                 43,000	381.57	$            45.15	336.42	42,664
2.00	42,664	381.57	$            44.80	336.77	42,327
3.00	42,327	381.57	$            44.44	337.13	41,990
4.00	41,990	381.57	$            44.09	337.48	41,652
5.00	41,652	381.57	$            43.73	337.84	41,314

116.00	1,902	381.57	$              2.00	379.57	1,522
117.00	1,522	381.57	$              1.60	379.97	1,142
118.00	1,142	381.57	$              1.20	380.37	762
119.00	762	381.57	$              0.80	380.77	381
120.00	381	381.57	$              0.40	381.17	0