Compound Interest-10th Grade-3

Find the nominal rate of interest which is equivalent to 8% effective
rate of interest when intrest is compounded half-yearly.

Solution: Let the nominal rate = R%

Number of conversation in a year (n) = 2

Effective rate = (1 + R/100n)ⁿ - 1

By the condition,

{1 + R/(100*2)}ⁿ - 1 = 8/100

or, {1 + R/(100*2)}ⁿ = 1 + 8/100

or, {1 + R/(100*2)}ⁿ = 108/100

or, 1 + R/200 = (1.08)^1/2

or, R/200 = (1.08)^1/2 - 1

or, R = 200 [(1.08)^1/2 - 1]

or, R = 200 [1.039 – 1]

So, R = 200 * 0.039 = 7.8

So, the required nominal rate of interest = 7.8%