Question

If you don’t repay a loan, and a lot of time passes, the debt can grow to unmanageable proportions, as happened to an unfortunate borrower in Melbourne. A grandmother has been forced to put her house up for sale after she ended up owing a massive $83 000 —on a $15 000 loan. Andrea lane, 57, borrowed the money in 2002 to pay for her father’s funeral and to buy a new oven for her Clayton home. But she could not meet the cost of the loan and 18 years later, the amount she owed had grown to $83 000 … Andrea said: ‘I borrowed the money when I was grieving for my father. I just signed the papers.’

a) Based on original loan of $15000, calculate the monthly repayments to be repaid over 5 years. Assume an interest rate of 25% p.a.

Andrea can afford to pay $600 per month into the loan, and she has been able to negotiate a new interest rate of 8% p.a.

b) How long would it take Andrea to repay the loan?

c) If she cannot afford to increase her current repayments, and is unable to negotiate a better interest rate, recommend a strategy to reduce the total length of time to repay the loan? Based on this strategy, how much interest would she save?

Answer 1

Given:

Loan Amount = $ 15,000

Interest rate = 25% p.a.

Tenure = 5 years

Using PMT formula in Excel, we can calculate the amount of Monthly repayments.

rate = interest rate per period = 25%/*12

nper= Total number of periods = 5 * 12 = 60 months

pv is the Present Value of the Loan = 15000

Loan amt	15000
Interest	25%
Tenure	60
EMI	PMT(rate,nper,pv)
EMI	PMT(25%/12,60,-15000)

Monthly repayments = $ 440.27

Solution b:

Andrea can afford to pay $600 per month into the loan, and she has been able to negotiate a new interest rate of 8% p.a.

Tenure=?

In order to calculate tenure of te loan, we can use NPER formula in Excel as follows:

NPER(rate, pmt, pv)

rate is the interest rate per period = 8%/12,

pmt is the value of monthly installment = 600,

pv is the present value of the loan = 15000

Loan amt	15000
Interest	8%
EMI	600
NPER	NPER(8%/12,600,-15000)
NPER	27.43929
No. of Years	=(27.43929/12) = 2.286608 years

The Loan Tenure will be 28 months or 2.33 years

Solution C:

Her current repayment installment per month = $ 600

She is unable to nogotiate with the interest rate, Hence, Interest rate = 25% p.a.

We can find the time period to repay the 15000 Loan amount @ 25% interest rate p.a. with monthly installments ,$ 600 using NPER formula

NPER(rate, pmt, pv)

rate is the interest rate per period = 25%/12,

pmt is the value of monthly installment = 600,

pv is the present value of the loan = 15000

Loan amt	15000
Interest	25%
EMI	600
NPER	NPER(25%/12,600,-15000)
NPER	35.68052 = 36
Number of Years	=36/12 = 3

Hence, she can repay the loan with 600 monthly installments in 3 years / 36 months

Interest she would save is given by the difference of the Future value of the payments 440.27 for 5 years and the future value of the payments 600 for 3 years at interest rate 25% per annum.

Future Value can be calculated using FV formula in Excel as follows:

FV(rate,nper,pmt)

rate is the interest rate per period = 25%/12,

nper is the number of periods

pmt is the value of the monthly installments

Interest rate	25%	25%
Tenure	60	36
EMI	440.27	600
FV	FV(25%/12,60,-440.27)	FV(25%/12,36,-600)
FV	$51,687.08	$31,701.59

The difference of the Future Values = 51687.08 - 31701.59 = 19,985.48

Hence, If she repays the loan with 600 monthly repayments in 3 years, she will save $ 19,985.48