Question

Jenny takes out a loan of $40,000 from Westpac for her small business at 6.00% p.a. compounded monthly and promises to pay it back over two years with equal monthly payments. Eight months after taking out the loan (just after the eighth payment is made), she stops making the payments for the following 6 months because business is bad. If there is a monthly penalty of $100 plus interest on the outstanding loan amount, what will her new monthly payments be when she restarts paying? Assume she takes 16 months to make the remaining payments, the interest rate remains unchanged, and interest is charged on unpaid penalties.

Answer 1

We need to find the equal monthly payment to be made

Using the PV of ordinary annuity formula,

PV(OA)=Pmt.*(1-(1+r)^-n)/r

& plugging in all the known values, as done below:

40000=Mthly Pmt.*(1-1.005^-24)/0.005

1772.82

With the above monthly payment,

we calculate the principal balance pending after the eighth payment

using the formula,

Future value of Remaining balance=FV of Original balance-Fv of annuity

ie.FV(Rem.Princ.Bal.=(PV*(1+r)^n)-((Pmt.*((1+r)^n-1)/r)

where,

PV=Present Value ,ie. Original balance of the loan= 40000

Pmt.=the monthly payment, 1772.82

r= rate /pmt. = 0.005

n= no.of pmt.periods = 8

Plugging in the above values,

FV(Rem.Princ.Bal.=(40000*(1+0.005)^8)-((1772.82*((1+0.005)^8-1)/0.005)

27195.03

Now, the new present Value at end of mth.=14(8+6) is 27195.03

along with PV of penalties 100*16 mths. =1600

The total PV=27195.03+1600=

28795.03

Now, calculating each of the 16 equal monthly payment

using the PV of ordinary annuity formula,

28795.03=Mthly Pmt.*(1-1.005^-16)/0.005

we get the new mthly. Pmt. As

1877.13

(ANSWER)