Question

A loan of £10,000 is repayable in 91 days at a simple rate of interest of 8% per annum. Assuming that 1 year is equivalent to 365 days, calculate: (i) the amount repayable in 91 days; (ii) the effective rate of discount per annum; (iii) the equivalent nominal rate of interest per annum convertible quarterly.

Answer 1

Answer: 2.08%

Explanation:

(i) The amount repayable in 91 days can be calculated using the formula:

Simple Interest = (Principal * Rate * Time) / 100

Here, Principal = £10,000, Rate = 8% per annum, Time = 91/365 years

Simple Interest = (10,000 * 8 * 91/365) / 100 = £182

The amount repayable in 91 days = Principal + Simple Interest = £10,000 + £182 = £10,182

(ii) The effective rate of discount per annum can be calculated using the formula:

Effective Rate of Discount = (Simple Interest / Principal) * (365 / Time)

Here, Simple Interest = £182, Principal = £10,000, Time = 91 days

Effective Rate of Discount = (182 / 10,000) * (365 / 91) = 2.936 %

(iii) The equivalent nominal rate of interest per annum convertible quarterly can be calculated using the formula:

Effective Rate of Interest = (1 + (Nominal Rate / m))^m - 1

Here, m = 4 (quarterly)

Effective Rate of Interest = (1 + (Nominal Rate / 4))^4 - 1 = 0.0835 or 8.35%

Solving for Nominal Rate:

Nominal Rate = (Effective Rate of Interest + 1)^(1/m) - 1

Nominal Rate = (0.0835 + 1)^(1/4) - 1 = 0.0208 or 2.08%

Therefore, the equivalent nominal rate of interest per annum convertible quarterly is 2.08%.