Weird loan

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,707
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.
 
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
 
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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