Loan repayment question (1 Viewer)

[luvotomy]

can someone please help me with the question below.

A loan of $6000 over 5 years at 15% p.a. interest, chraged monthly, is paid back in 5 yearly instalments. How much is each instalment, and how much money is paid altogether?

ans: $1835.68; $9178.40

 

[3unitz]

let
A = amount owing
I = yearly instalment
r = (1 + 15/100 . 1/12)^12 = 1.0125^12

after 1 year:
A = 6000r - I

after 2 years:
A = 6000r^2 - Ir - I

after 5 years:
A = 6000r^5 - Ir^4 - Ir^3 - ... - I
0 = 6000r^5 - Ir^4 - Ir^3 - ... - I (A = 0 after 5 years)
6000r^5 = I(r^4 + r^3 + ... + 1) <--- geometric series
6000r^5 = I(1 - r^5)/(1 - r)
I = 6000r^5(1 - r)/(1 - r^5)
~ $1835.68

total = 5I
~ $9178.41

 

[lyounamu]

can someone please help me with the question below.

A loan of $6000 over 5 years at 15% p.a. interest, chraged monthly, is paid back in 5 yearly instalments. How much is each instalment, and how much money is paid altogether?

ans: $1835.68; $9178.40

15% p.a. = 1.25% p.m.

Afer the first payment: 6000 x 1.0125^12 - AI
After the 2nd payment: (6000 x 1.0125^12 - AI) x 1.0125^12 - AI = 6000 x 1.0125^24 - AI(1 + 1.0125^12)
After the 5th payments: 6000 x 1.0125^60 - AI (1+1.0125^12+...+1.0125^48) = 0

Therefore, 6000 x 1.0125^60 = AI(1+1.0125^12 + ...+1.0125^48)
AI = $1835.68259...

Total amount = 5 . AI = $9178.4129...

Damn...I got beaten.

 

[munchiecrunchie]

hey guys can you punch that solution on 2 ur calculators, coz i can't actually seem to get the final answer, I can follow the solution but the calculators not giving me that answer . . .

 

[lyounamu]

hey guys can you punch that solution on 2 ur calculators, coz i can't actually seem to get the final answer, I can follow the solution but the calculators not giving me that answer . . .

I already did and I got them right.

I don't know how you didn't get it though.

Let me see:

6000 x 1.0125^60 = AI(1+1.0125^12 + ...+1.0125^48)
Therefore, AI = 6000 x 1.0125^60 divided by (1+1.0125^12 + ...+1.0125^48) where 1 = a and r = 1.0125^12 and n = 5. You use geometric sum formula here.

So you get:

AI = $1835.68259...

 

[luvotomy]

thanks guyss~~