Quantitative Problem: You need $10,000 to purchase a used car. Your wealthy uncle is willing to...

Quantitative Problem: You need $10,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 5 years, with the first payment to be made one year from today. He requires a 5% annual return. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent. $ How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent

Interest: $ ??

Principal repayment: $ ??

Expert Solution

Annual Instalment :
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	$ 10,000.00
Int rate per Anum	5.0000%
No. of Years	5

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 10000 / PVAF (0.05 , 5)
= $ 10000 / 4.3295
= $ 2309.75
Annual Instalment = $ 2309.75

Loan Aortization schedule:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$ 10,000.00	$ 2,309.75	$ 500.00	$ 1,809.75	$ 8,190.25
2	$ 8,190.25	$ 2,309.75	$ 409.51	$ 1,900.24	$ 6,290.02
3	$ 6,290.02	$ 2,309.75	$ 314.50	$ 1,995.25	$ 4,294.77
4	$ 4,294.77	$ 2,309.75	$ 214.74	$ 2,095.01	$ 2,199.76
5	$ 2,199.76	$ 2,309.75	$ 109.99	$ 2,199.76	$ -

Opening Balance = Previous month closing balance
EMI = Instalment calculated
Int = Opening Balance * Int Rate
Principal repay = Instalment - Int
Closing Balance = Opening balance - Principal Repay

From Loan Amortization Schedle,

Int in First Payment = $ 500 ( $ 10000 * 5% )

Principal Repayment = $ 2309.75 - $ 500

= $ 1809.75

jeff jeffy answered 1 year ago

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