# Weird loan

#### Denis

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 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
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...