A loan of ₹2,550 is to be paid back in two equal half-yearly instalments. How much is each instalment if the interest is compounded half-yearly at 8% p.a.?

Given:
Principal (P) = ₹2,550

Annual interest rate = 8% p.a.

Since interest is compounded half-yearly, the rate per half-year is:

R=
2
8%
​
=4%
Number of installments (n) = 2

Let each installment be X. The present value of the installments must equal the loan amount:

P=
(1+
100
R
​
)
1

X
​
+
(1+
100
R
​
)
2

X
​

Here, 1+
100
R
​
=1+
100
4
​
=1+
25
1
​
=
25
26
​
.

Substituting this into the equation:

2550=
25
26
​

X
​
+
(
25
26
​
)
2

X
​

2550=
26
25X
​
+
676
625X
​

Taking the common denominator as 676:

2550=
676
25×26×X+625X
​

2550=
676
650X+625X
​

2550=
676
1275X
​

X=
1275
2550×676
​

Since 2550=2×1275:

X=2×676=1,352
Therefore, each installment is ₹1,352.