Question

In: Finance

You want to buy a car, and a local bank will lend you $25,000.The loan...

You want to buy a car, and a local bank will lend you $25,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 5% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

Monthly loan payment: $

EAR: %



Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.

aAn initial $700 compounded for 1 year at 9%.

$   

bAn initial $700 compounded for 2 years at 9%.

$   

cThe present value of $700 due in 1 year at a discount rate of 9%.

$   

dThe present value of $700 due in 2 years at a discount rate of 9%.

Solutions

Expert Solution

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 $             25,000.00
Int rate per Month 0.4167%
No. of Months 60

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 25000 / PVAF (0.0042 , 60)
= $ 25000 / 52.9907
= $ 471.78
Effective Annual Rate = ( 1 + r ) ^ n - 1
r = Int Rate per period
n = No.of periods per anum

Particulars Amount
Ret period 0.4167%
No. of periods    12.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.004167 ) ^ 12 ] - 1
= [ ( 1.004167 ) ^ 12 ] - 1
= [ 1.0512 ] - 1
= 0.0512
I.e EAR is 5.12 %

Part B:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

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

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

a)

Particulars Amount
Present Value $                700.00
Int Rate 9.0000%
Periods 1

Future Value = Present Value * ( 1 + r )^n
= $ 700 ( 1 + 0.09) ^ 1
= $ 700 ( 1.09 ^ 1)
= $ 700 * 1.09
= $ 763

b)

Particulars Amount
Present Value $                700.00
Int Rate 9.0000%
Periods 2

Future Value = Present Value * ( 1 + r )^n
= $ 700 ( 1 + 0.09) ^ 2
= $ 700 ( 1.09 ^ 2)
= $ 700 * 1.1881
= $ 831.67

c)

Particulars Amount
Future Value $                 700.00
Int Rate 9.0000%
Periods 1

Present Value = Future Value / ( 1 + r )^n
= $ 700 / ( 1 + 0.09 ) ^ 1
= $ 700 / ( 1.09 ) ^ 1
= $ 700 / 1.09
= $ 642.2

d)

Particulars Amount
Future Value $                 700.00
Int Rate 9.0000%
Periods 2

Present Value = Future Value / ( 1 + r )^n
= $ 700 / ( 1 + 0.09 ) ^ 2
= $ 700 / ( 1.09 ) ^ 2
= $ 700 / 1.1881
= $ 589.18


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