Question

renu borrows a sum of 50440 at 10%pa compounded half yearly. She pays the amount in three equal half yearly installments of rs x. Find the value of x?

Answer 1

Given :

The sum of money borrowed = p = Rs 50,440

The rate of interest = r = 10 % pa compounded half yearly

The amount is paid in three equal half yearly installments of Rs x

To Find :

The value of x

Solution :

From Compound Interest method

Amount = Principal × $(1+\dfrac{rate}{2 \times 100}) ^{2 \times time}$

              = p $(1+\dfrac{rate}{2 \times 100}) ^{2 \times time}$

Now,

When the amount is paid in three equal half yearly installments of Rs x

i.e  p $(1+\dfrac{rate}{2 \times 100}) ^{2 \times time}$ = x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 3}$ +   x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 2}$ +  x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 1}$

or,   p $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 3}$ = x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 3}$ +   x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 2}$ +  x ×  $(1+\dfrac{rate}{2 \times 100}) ^{2 \times 1}$

Or,   p $(1+\dfrac{rate}{200}) ^{6}$ = x ×  $(1+\dfrac{rate}{200}) ^{6}$ +   x ×  $(1+\dfrac{rate}{200}) ^{4}$ +  x ×  $(1+\dfrac{rate}{200}) ^{2}$

Or, 50400 ×  $(1+\dfrac{10}{200}) ^{6}$ = x ×  $(1+\dfrac{10}{200}) ^{6}$ +   x ×  $(1+\dfrac{10}{200}) ^{4}$ +  x ×  $(1+\dfrac{10}{200}) ^{2}$

Or, 50400 × 1.34 =  x × 1.34 +  x × 1.21 +  x × 1.1

Or,  50400 × 1.34 =  x × ( 1.34 + 1.21 +1.1 )

Or, 50400 × 1.34 =  x × 3.65

Or, 67536 =  x × 3.65

i.e            x = $\dfrac{67536}{3.65}$

∴             x = Rs 18503

Hence, The value of x is Rs 18503   . Answer