Question

Assume that you want to borrow $800,000 in order to purchase a new car. As you are a fresh graduate, you can only find one lender, Come-On Finance Limited, willing to grant you an auto loan. In fact, a friend of yours can also give you a helping hand. You are now comparing the following loans under different terms offered by the two parties. Loan 1: Borrow $800,000 from Come-On Finance as an add-on 4% simple interest loan, with quarterly payments over five years.' Loan 2: Borrow $800,000 for six years from your friend, who agrees to charge you simple interest based on 3% annual interest rate, and you only need to repay the entire loan at the end of the period. + t a. Calculate the total amount of interest to be paid under each loan terms b. Compute the respective annual percentage rate (APR). c. Decide which loan you should choose based on the results from parts (a) and (b).

Answer 1

Solution:-

a)Calculation of total interest Payable on Both the Loan

Simple Interest Calculation Formula is A=P(1+rt)

Here,A=Final Amount Payable

P=Principal Amount

r= Rate of Interest

t= Tenure of Loan

Total Interest Payable is:-

In case of Loan 1:-

A=P(1+rt)

A=$800000(1+.04*5)

A=$800000(1.2)=9,60,000

Interest Amount=Total Payable –Principal Amount=$9,60,000-$8,00,000=$1,60,000

In case of Loan 2:-

A=P(1+rt)

A=$800000(1+.03*6)

A=$800000(1.18)=$9,44,000

Interest Amount=Total Payable-Principal Amount=$9,44,000-$8,00,000=$1,44,000

b)Computation of Annual Percentage Rate(APR)

APR  is the annual rate of interest that is paid on investment or loan,without taking in to account the compounting of interest within that year.APR is calculated by multiplying the periodic interest rate by the no.of periods in a year in which the periodic rate is applied.

APR=((Total Interest/Principal Amount)/Total No.of days in loan term)/365*100

We can calculate APR by using the above formula.But ,in the above two case there is no other charges are payable for the loan.So that the APR shall be the same as Interest Rate.

APR for Loan 1=4%

APR for Loan 2=3%

c)From the above problem second loan having less interest amount is payable than Loan 1.But as per the condition of second loan the loanee shall be payable full amount at the time of closing.Even though the payment is in quarterly in the second loan,the interest payable shall not reduced with the total amount of interest payable.And also by comparing the Future value of money of both the loan ,the loan second will be more beneficial to us.So,I will choose the second option as car Loan.