Weird loan

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,468
A $1000.00 loan over a 12month period, at rate 1% per month.
Monthly payments are p per month for 1st 4 months,
no payments next 4 months, then p per month for last 4 months.
Code:
MONTH PAYMENT INTEREST BALANCE 
  0                    1000.00 
  1     -p     10.00     ? 
  2     -p       ?       ? 
  3     -p       ?       ? 
  4     -p       ?       ? 
  5     0.00     ?       ? 
  6     0.00     ?       ? 
  7     0.00     ?       ? 
  8     0.00     ?       ? 
  9     -p       ?       ? 
 10     -p       ?       ? 
 11     -p       ?       ? 
 12     -p       ?      0.00
Calculate p.
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,138
A $1000.00 loan over a 12 month period, at rate 1% per month.
Monthly payments are p per month for 1st 4 months,
no payments next 4 months, then p per month for last 4 months.
Code:
MONTH PAYMENT INTEREST BALANCE 
  0                    1000.00 
  1     -p     10.00     ? 
  2     -p       ?       ? 
  3     -p       ?       ? 
  4     -p       ?       ? 
  5     0.00     ?       ? 
  6     0.00     ?       ? 
  7     0.00     ?       ? 
  8     0.00     ?       ? 
  9     -p       ?       ? 
 10     -p       ?       ? 
 11     -p       ?       ? 
 12     -p       ?      0.00
Calculate p.
1000*(1.01)^12 = p*(1.01)^11 + p(1.01)^10 + p(1.01)^9 +p(1.01)^8 + p(1.01)^3 + p(1.01))^2 + p(1.01) + p

p*(1.01)^11 + p(1.01)^10 + p(1.01)^9 +p(1.01)^8 + p(1.01)^3 + p(1.01))^2 + p(1.01) + p

= p*(1.01)^8 * [(1.01)^4-1]/0.01 + p * [(1.01)^4-1]/0.01

= p*(4.060401)*[(1.01)^8 + 1]

= p * 8.457233

p = 133.238 = 133.24


If the person paid all 12 months, his bill would have been 88.85
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,468
Yer ready for the CEO job of the Loan Calculation Division at the Khan Bank!

a = 1000
i = .01

r = 1 + i
k = (r^4 - 1) / i

a*r^12 = p(k*r^8) + p*k
ar^12 = p(kr^8 + k)
p = ar^12 / [k(r^8 + 1)]
p = 133.238018...
 
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