Question

Derek borrows $299,931.00 to buy a house. He has a 30-year mortgage with a rate of 5.55%. After making 97.00 payments, how much does he owe on the mortgage?

Answer format: Currency: Round to: 2 decimal places.

Derek borrows $36,284.00 to buy a car. He will make monthly payments for 6 years. The car loan has an interest rate of 5.24%. What will the payments be?

Answer format: Currency: Round to: 2 decimal places.

Derek borrows $37,025.00 to buy a car. He will make monthly payments for 6 years. The car loan has an interest rate of 5.97%. After a 11.00 months Derek decides to pay off his car loan. How much must he give the bank?

Answer format: Currency: Round to: 2 decimal places.

Suppose you deposit $1,006.00 into an account 5.00 years from today that earns 12.00%. It will be worth $1,888.00 _____ years from today.

Answer format: Number: Round to: 2 decimal places.

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	$          299,931.00
Int rate per Month	0.4625%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 299931 / PVAF (0.0046 , 360)
= $ 299931 / 175.1528
= $ 1712.4

Mortgage Balance after 97 Months:

Particulars	Amount
Loan Amount	$ 299,931.00
Int rate per Month	0.4625%
No. of Months	360
Outstanding Bal after	97
EMI	$      1,712.40
Payments Left	263

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1712.4 * [ 1 - ( 1 + 0.004625 ) ^ - 263 ] / 0.004625
= $ 1712.4 * [ 1 - ( 1.004625 ) ^ - 263 ] / 0.004625
= $ 1712.4 * [ 1 - 0.297134 ] / 0.004625
= $ 1712.4 * [ 0.702866 ] / 0.004625
= $ 260235.19

r = Int Rate per period
n = Balance No. of periods

Part B:

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	$             36,284.00
Int rate per Month	0.4367%
No. of Months	72

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 36284 / PVAF (0.0044 , 72)
= $ 36284 / 61.6656
= $ 588.4

Part C:

Particulars	Amount
Loan Amount	$             37,025.00
Int rate per Month	0.4975%
No. of Months	72

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 37025 / PVAF (0.005 , 72)
= $ 37025 / 60.3911
= $ 613.09
Balance after 11 Months:

Particulars	Amount
Loan Amount	$    37,025.00
Int rate per Month	0.4975%
No. of Months	72
Outstanding Bal after	11
EMI	$         613.09
Payments Left	61

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 613.09 * [ 1 - ( 1 + 0.004975 ) ^ - 61 ] / 0.004975
= $ 613.09 * [ 1 - ( 1.004975 ) ^ - 61 ] / 0.004975
= $ 613.09 * [ 1 - 0.738804 ] / 0.004975
= $ 613.09 * [ 0.261196 ] / 0.004975
= $ 32188.27

r = Int Rate per period
n = Balance No. of periods

Part D:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$      1,006.00
Future Value	$      1,888.00
Int Rate per period	12.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1888 = $ 1006 ( 1 + 0.12 ) ^ n
( 1 + 0.12 ) ^ n = $ 1888 / $ 1006
1.12 ^ n = 1.8767
Take Log on Both sides
Log ( 1.12 ^ n ) = Log ( 1.8767 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.12 ) = Log ( 1.8767 )
n * 0.0492 = 0.2734
n = 5.56

It will be $ 1888 after 10.56 Years ( 5 + 5.56)