Question

Dupu U No Spac. Heading 1 Heading 2 A BLE ABLE Aabbed MORGET ABbccbr ARCABECEDAABEcco ABCD A Subtitle Subtlem. Emphasis intense . Strong Quote intense . Subtle Red Intense Re Book Title A Y A . . . Normal Title Font Paragraph 1. You have purchased a used car for $3000 with a loan at 6% APR, compounded monthly. You have agreed to repay the loan in 12 equal end-of-month payments. The payments are made at the end of each month. After you have made the eighth payment, you decide to repay the loan in full when the next payment is due. The bank imposes a penalty of 20% of the remaining balance for early payment. (i) What is the payment you make when you close the loan? (ii) What are the payments made towards the principal in month 1 and month 3? (iii) Redo part (1) if you received interest free loan from the bank?

please show all steps.

Answer 1

car amount (principal) = 3000

rate of interest (r) = 6% apr that is 0.5% per month

period of loan (N) = 12 month

total amount to be paid (a)= ?

A = P(1+R/100)^N

Put the Values

A= 3000(1+0.5/100)¹²

= 3000(100.5/100)¹²

= 3000*1.06

= $ 3185

therefor each installment will be = 3185/12 = $265.42

as 8 installment are paid balance loan available is = 3185-(265.42*8) = 3185 - 2123 = 1062

i) to close loan amount need to be paid is

=1062+(1062*20%)

= $1274

ii) amount paid towards principal

in first year payment towards principal will be $ 250

in third year payment towards principal will be $ 250

iii) if loan is interest free

balance remain will be

= 3000/12 = $250

as eight payments are made

=250*8 = $2000

payment towards principal will be

= (3000-2000)

=1000

as penalty is 20%

final amount will be

=1000+(1000*20%)

=1000+200

= $ 1200