Question

a. You want to buy a car, and a local bank will lend you $30,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 7% 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:

b. What is the present value of a $400 perpetuity if the interest rate is 9%? If interest rates doubled to 18%, what would its present value be? Round your answers to the nearest cent.

Present value at 9%: $  

Present value at 18%: $

c. You borrow $335,000; the annual loan payments are $32,607.68 for 30 years. What interest rate are you being charged? Round your answer to the nearest whole number.

Answer 1

Part A:

Particulars	Amount
Loan Amount	$             30,000.00
Int rate per Month	0.5833%
No. of Months	60

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 30000 / PVAF (0.0058 , 60)
= $ 30000 / 50.502
= $ 594.04

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

EAR:

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.005833 ) ^ 12 ] - 1
= [ ( 1.005833 ) ^ 12 ] - 1
= [ 1.0723 ] - 1
= 0.0723
I.e EAR is 7.23 %

Part B:

If Int rate is 9%:

PV of Perpectuity = Cash Flow / Int Rate

= $ 400 / 9%

= $ 4444.44

If Int Rate is 18%:

PV of Perpectuity = Cash Flow / Int Rate

= $ 400 / 18%

= $ 2222.22

Part C:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

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

Here Instalment amount is Annuity.

Particulars	Amount
PV Annuity	$    335,000.00
Time Period	30.00
Cash Flow	$      32,607.68

PV of Annuity = Cash flow * PVAF(r%, n)
PVAF(r%, n ) = PV of Annuity / Cash Flow
= $ 335000 / $ 32607.68
= 10.2737

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

The Rate at which PVAF for 30 Periods will be equal to 10.2737 will be the answer.
PVAF(9%30) = 10.2737

Thus Annual int rate is 9% per anum.