Question

Assume that Jane wants to buy a new car and needs to borrow$15000 from Scotiabank.

Calculate the annual payment to the Bank for each of following cases. In each case, show all your work. Discuss the relationship between the annual payment and the interest rate.

If she wants to pay off the loan in 15 years and interest rate is 5%

If she wants to pay off the loan in 10 years and interest rate is 4%

If she wants to pay off the loan in 20 years and interest rate is 10%

If she wants to pay off the loan in 10 years and interest rate is 5%

pls step by step

Answer 1

Annual Instalment :
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

Part A:

Particulars	Amount
Loan Amount	$             15,000.00
Int rate per Anum	5.0000%
No. of Years	15

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 15000 / PVAF (0.05 , 15)
= $ 15000 / 10.3797
= $ 1445.13

Part B:

Particulars	Amount
Loan Amount	$             15,000.00
Int rate per Anum	4.0000%
No. of Years	10

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 15000 / PVAF (0.04 , 10)
= $ 15000 / 8.1109
= $ 1849.36

Part C:

Particulars	Amount
Loan Amount	$             15,000.00
Int rate per Anum	10.0000%
No. of Years	20

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 15000 / PVAF (0.1 , 20)
= $ 15000 / 8.5136
= $ 1761.89

Part D:

Particulars	Amount
Loan Amount	$             15,000.00
Int rate per Anum	5.0000%
No. of Years	10

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 15000 / PVAF (0.05 , 10)
= $ 15000 / 7.7217
= $ 1942.57