Question

Suppose you want to buy a $148,000 home. You found a bank that offers a 30-year loan at 3.9% APR. What will be your monthly payment? (Round to the nearest cent.)

$

How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.)

$

Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.)

$

How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.) $ How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)

$

Answer 1

Part A:

EMI :
EMI or Instalment is sum of money due as one of several equal payments for loan/ Mortgage taken today, spread over an agreed period of time.

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

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Particulars	Amount
Loan Amount	$          148,000.00
Int rate per Month	0.3250%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 148000 / PVAF (0.0033 , 360)
= $ 148000 / 212.0134
= $ 698.07

Part B:

Total Amount Paid:
Total Amount paid = Instalment * No. of Instalments
= $ 698.07 * 360
= $ 251304.82

Part C:

Particulars	Amount
Loan Amount	$          148,000.00
Int rate per Month	0.3250%
No. of Months	300

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 148000 / PVAF (0.0033 , 300)
= $ 148000 / 191.4495
= $ 773.05

Part D:

Total Amount Paid:
Total Amount paid = Instalment * No. of Instalments
= $ 773.05 * 300
= $ 231914.95