How to find amount of final payment

Question

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.

But the given answer is 3580(app.). Where i am wrong? Please help me.

callculus42 · Accepted Answer · 2018-05-09T13:28:08.170

1

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 $1.06$.

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

edited May 09 '18 at 13:28

answered May 06 '18 at 16:40

callculus42

30,550

from where 2000 come? – Kanwaljit Singh May 09 '18 at 05:04
@KanwaljitSingh Good catch. I mean´t $20,000$ obviously – callculus42 May 09 '18 at 13:27
Thank you so much – Raj Kumar Singh May 21 '18 at 15:01
@RajKumarSingh You´re welcome – callculus42 May 21 '18 at 15:02
@callculus please help me with this question also https://math.stackexchange.com/questions/2790124/simple-interest-tricky-question – Raj Kumar Singh May 21 '18 at 15:13
@RajKumarSingh I´ve noticed the question already. But at the moment I don´t get the answer of the solution. – callculus42 May 21 '18 at 15:14
SI = p * r * t/100 – Raj Kumar Singh May 21 '18 at 15:40
SI = 100, p = 350. – Raj Kumar Singh May 21 '18 at 15:40
@callculus can you please give me hint on this. Demand for a product is given by the function $q=\frac{10}{\sqrt{4p+1}}$. Find the marginal demand at p=6. – Raj Kumar Singh May 23 '18 at 08:27
@RajKumarSingh I´ve noticed that you have already got an answer. – callculus42 May 23 '18 at 15:38

How to find amount of final payment

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