Question

x=3000

P 1.4 = A businessman borrowed money from a bank to finance his personal jet. The bank loan terms allowed him to defer payments for six months and then to make 36 equal end of payments thereafter. The original bank loan was $9600+X with an interest rate of 12% compounded monthly. After sixteen monthly payments, he finds himself in trouble due to business loss and went to a loan company for assistance in lowering his monthly payments. Luckily, he got the deal and the loan company offered to pay his debts in one lump sum, provided that he pays the company $208 per month for the next 36 months. Calculate the monthly rate of interest is the loan company charging on this transactions? Note that X is the last digit of your University ID and its in 1000. For example, if student ID is 3, the value of X is $ 3000. ****** ***

Answer 1

Loan amount = $ 9,600 + 8,000 = $ 17,600

First payment will be made at the end of 7th month. Number of payments = 36

Interest rate = 12% compunded monthly = 1% per month

Loan amount after 6 months = 17,600 ×1.01^6 = 18,682.45

Now calculating the equal monthly payment.

A = 18,682.75(A/P, 1%,36) = A= 18, 682.75 x 0.01 1 - 1.01-36 = A= 18, 682.75 x 0.0332143 A$ 620.53

Under first plan he was required to make a monthly payment of $ 620.53.

After 16 monthly payment loan balance can be determined as follows. Number of payments yet to be paid = 36 - 16 = 20 payments.

Loan balance after 16 payments = 620.53(P/A,1%,20)

= 620.53 × 18.0455

= $ 11,197.89

Under new loan he will be required to make a payment of $ 208 for 36 months.

11, 197.89 = 208(P/A, 1%, 36) (P/A, i%, 36) 11,197.89 208 (P/A, 1%,36) = 53.8306 = (P/A, i%, 36) – 53.8306 = 0

We can determine the value of i using trial and error method. I have tried a number of interest rate but I was unable to locate so I tried it using excel. Refer the screenshot of excel along with the formula

fx =RATE(36,208,- BM6 ,0) < BL BM BN BO BP 2 3 Loan 4 5 After 6 months Installment After 16 payments Rate $ 17,600.00 $ 18,682.75 $ 620.53 11,197.89 -2.03° 6 7

Using excel getting rate = - 2.03% per month.

It is obvious because earlier we were paying around $ 620 and now even less than 1/3rd amount. Thus, I will rely on excel and by plugging in this in the equation we can verify it

(Ρ/Α, 1%, 36) = 1- (1 + (-0.0203)-36 -0,0203 53.8136

Thus, interest rate = - 2.03% per month.