Respuesta :
a. Total Interest on Loan is $8,640
b. Total Cost of Car to Richard is $26,640
c. Monthly Payment under add on Interest loan is $320.
d. Annual Percentage Rate=1.42% x 12=17.04%
a. Total Interest on Loan is $8,640
Total Interest on Loan=Principal Amount Borrowed*Interest Rate Term of Loan
=$14,400 x10% x6
=$8,640
b. Total Cost of Car to Richard is $26,640
=Purchase Price of Car + Total Interest Loan
=$18,000+$8,640
=$26,640
c. Monthly Payment under add on Interest loan is $320.
Monthly Payment under add on Interest loan
=Principal + Interest No of Months
14, 400 + 8,640 12 x 6
=23,040 72
=$320.
d. Annual Percentage Rate=1.42% x 12=17.04%
Annual Percentage Rate is also know as effective Interest Rate we can calculate it using PV formula
PV = C x PV
Where PV =Principal Amount=$14,400
C=Monthly Payment=$320
N=No. of month=72
I=Rate of interest per month
14, 400 = 320 + PV
PV (I, 72) = 45
We would have to calculate rate of interest per month at which Present Value Annuity Factor for 72 months is 45.
Let's Calculate i by trial and error method
Let Calculate PV (1%,72)=51.1504
PV(1.5%,72)=43.8447
We can calculate Rate of interest
If rate if interest increased by 0.5% ,then PV reduced by 7.3057
By how much % rate of interest is required to be increase so that PV reduces by 6.1504
6.1504 x 0.5 7.3057
=0.4209%
Rate of interest per month=1%+0.42%=1.42%
Annual Percentage Rate=1.42% x 12=17.04%
Complete Question
After visiting several automobile dealerships, Richard selects the car he wants. He likes its $18,000 price, but financing through the dealer is no bargain. He has $3,600 cash for a down payment, so he needs a loan of $14,400. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $14,400 for a period of six years at an add-on interest rate of 10 percent.
a. What is the total interest on Richard’s loan?
b. What is the total cost of the car?
c. What is the monthly payment?
d. What is the annual percentage rate (APR)?
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