Answer to Question #133279 in Financial Math for Rikansha

Question

A loan of $1400 is due in 1 year at a simple interest rate of 12%. Partial payments of $400 in 2 months, $25 in 6 months, and $700 in 8 months are made
A. Construct a timeline clearly showing the timing of the debt and all repayments.
B. Determine the balance due at the end of the 12 months using the merchant rule
C. Determine the balance due at the end of the 8 months using the declining balance method

Answer 1

B. By merchant method:

Total amount to be paid at the end of year one=1400*(1+(12/100)=$1568

Total debt paid at the end of 12 months =400+25+700=$1125

$\therefore$ Balance due of 12 months by merchant =1568-1125

=$443

At the end of 12 months,$ 443 is the balance by merchant rule.

C.By declining balance method assuming that monthly EMI schedule is being calculated at the end of 8 months

For monthly EMI calculation formulae = I * P[1-(1+I)^-n]

where;

I=interest rate per period

P=principal(in our case 1400)

n=term of loan period(12 months)

$\therefore$ monthly EMI=0.01*1400(1-(1.01)^-12)

=124

$\therefore$ by monthly EMI calculation for declining method the balance method the balance at the end of 8 months is (4*124)=$496