Question

1)

Ali had a loan of $144,000 and made payments of $2,750 at the end of every month to settle it. If he received the loan at 4.32% compounded monthly, what was the balance on the loan at the end of three years?

2)Lucy received a loan of $9,000 at 4.50% compounded quarterly. She had to make payments at the end of every quarter for a period of 1 year to settle the loan.

a. Calculate the size of payments.

Round to the nearest cent

b. Fill in the amortization schedule, rounding the answers to two decimal places.

Payment Number	Amount Paid	Interest Portion	Principal Portion	Principal Balance
0				$9,000.00
1
2
3
4
Total

Answer 1

Part 1:

EMI :

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

2750 = 144000 / PVAF(r%, n)

PVAF(0.36%, n) = 144000 / 2750

= 52.3636

The period at which PVAF @0.36% is 52.3636 is the answer.

At 58 Months, PVAF is = 52.2606

At 59 Months PVAF is = 53.0695

Thus No. of periods :

= 58 + [ (52.3636 - 52.2606) / ( 53.0695 - 52.2606 ) ]

= 58 + [ 0.103 / 0.8089 ) ]

= 58 + 0.13

= 58.13 Months

Part 2:

EQI :

EQI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

= $ 9000 / PVAF ( 1.125% , 4)

= $ 9000 / 3.89

= $ 2313.64

Loan AMortization:

Quarter	Opening Bal	Instalment	Int	Principal Repay	Closing Bal
1	$ 9,000.00	$ 2,313.64	$ 101.25	$ 2,212.39	$ 6,787.61
2	$ 6,787.61	$ 2,313.64	$    76.36	$ 2,237.27	$ 4,550.34
3	$ 4,550.34	$ 2,313.64	$    51.19	$ 2,262.44	$ 2,287.90
4	$ 2,287.90	$ 2,313.64	$    25.74	$ 2,287.90	$             -

Pls do rate, if the answer is correct and comment, if any further assistance is required.