In: Finance
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%.
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