An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Here’s the detailed explanation:
The financier claims to be lending at simple interest, but actually compounds interest semi-annually. To find the effective rate, we’ll calculate the interest accrued in one year.
Simple Interest (SI) for 1 year:
SI = (Principal × Rate × Time) / 100
= (P × 10% × 1)
= 0.1P
Compound Interest (CI) for 1 year (compounded semi-annually):
CI = P × (1 + (Rate/2))^2 – P
= P × (1 + (10%/2))^2 – P
= P × (1 + 5%)^2 – P
= P × (1.05)^2 – P
= 1.1025P – P
= 0.1025P
Effective Rate of Interest:
Effective Rate = (CI / P) × 100%
= (0.1025P / P) × 100%
= 10.25%
Therefore, the effective rate of interest is 10.25%.
