Question

Mr. Paul borrows Rs. 20000 on condition to repay it with C.I. at 5% p.a in annual installments of Rs. 2000 each. The number of years for the debt to be paid off is?

  

Answer 1

Given that,

Periodic payment = 2000

Amount of loan = 20000

Periodic interest rate= 5% =0.05

We need to calculate the number of periods

Using formula of periodic payment

$A=P\dfrac{r(1+r)^n}{(1+r)^n-1}$

Where, A = Periodic payment

P = Amount of loan

r = Periodic interest rate

Put the value into the formula

$2000=20000\times\dfrac{0.05(1+0.05)^n}{(1+0.05)^n-1}$

$2000=1000\times\dfrac{(1.05)^n}{(1.05)^n-1}$

$2(1.05)^n-2=(1.05)^n$

$(1.05)^n=2$

Taking log

$ln(1.05)^n=ln(2)$

$n\ ln(1.05)=ln(2)$

$n=\dfrac{ln(2)}{ln(1.05)}$

$n=14.2\ years$

It will take 15 years to repay the loan.

Hence, The number of years for the debt to be paid off is 15 years.

Answer 2

Answer:

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