# How to find amount of final payment

A man borrowed Rupees 20,000 at 6% C.I (compound interest) promising to repay Rupees 5000 at the end of first 4 years to reduce the principal and interest and to pay the balance at the end of the 5th year. Find the amount of his final payment.

Here i am using the formula of annuity.

$P = x \frac{[(1+i)^n-1]}{i}$

Above n = 4, i = 0.06 and x = 5000

I am getting 21873.08, After subtracting 20000 we left with 1873.08.

You have to transform the present value of $20000$ into the future value.

$$D_4=\underbrace{20000\cdot 1.06^4}_{\texttt{future value}}-\underbrace{5000\cdot \frac{(1+0.06)^4-1}{0.04}}_{\texttt{future value of the 4 payments}}=3376.46$$

This are the remaining debts at the end of the fourth years. This have to be transformed into the value at the end of the fifth year. This can be made by multiplying it by $1.06$.

$$D_5=D_4\cdot 1.06=3376.46\cdot 1.06=3579.05\approx 3580$$

• from where 2000 come? – Kanwaljit Singh May 9 '18 at 5:04
• @KanwaljitSingh Good catch. I mean´t $20,000$ obviously – callculus May 9 '18 at 13:27
• Thank you so much – Raj Kumar Singh May 21 '18 at 15:01
• @RajKumarSingh You´re welcome – callculus May 21 '18 at 15:02
• @callculus please help me with this question also math.stackexchange.com/questions/2790124/… – Raj Kumar Singh May 21 '18 at 15:13