Question

Instructions	Complete the following problems using either a financial calculator or a spreadsheet program. Do not use interim rounding, state your answers as positive values, to two decimal places for dollar or period values and four places for percentages stated as decimals; do not label answers with symbols such as $ or %. For example, 10.5% should be input as .1050.

1. Jacinda Herschel wants to buy a car and determines she can afford to pay $367.47 a month for a 3 year loan. The rate on such a loan is 0.0528. How much money can Jacinda borrow?

2. Brian Burkhardt is planning to purchase a home and expects to borrow $704,522 to mortgage the purchase, Given a 30-year mortgage has a rate of 0.0273, the monthly payment Brian can expect to pay is:

3. An investment with semi-annual compounding has an effective rate of 0.1119. The nominal rate is:

Answer 1

Part 1:

Max Loan = PV of EMIs

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$               367.47
Int Rate	0.4400%
Periods	36

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 367.47 * [ 1 - [(1+0.0044)^-36]] /0.0044
= $ 367.47 * [ 1 - [(1.0044)^-36]] /0.0044
= $ 367.47 * [ 1 - [0.8538]] /0.0044
= $ 367.47 * [0.1462]] /0.0044
= $ 12209.61
Max Loan that can be taken today is $ 12209.61

Part 2:

Particulars	Amount
Loan Amount	$         7,04,522.00
Int rate per Month	0.2275%
No. of Months	360

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 704522 / PVAF (0.0023 , 360)
= $ 704522 / 245.5901
= $ 2868.69

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

Part 3:

Particulars	Amount
Effective Annual rate	11.1900%
No. of periods per anum	2.0000

APR = [ [ ( 1 + EAR )^( 1 / n ) ] - 1 ] * n
= [ [ ( 1 + 0.1119 )^( 1 / 2 ) ] - 1 ] * 2
= [ [ ( 1.1119 )^( 1 / 2 ) ] - 1 ] * 2
= [ [ 1.0545 ] - 1 ] * 2
= [ 0.0545 ] * 2
= 0.109
= 10.9 %

Annual int rate ( APR ) is 10.9 % per anum