Question

Find the amount of interest that $5000 deposited on August 27, 2018 will earn, if the money is withdrawn on May 4, 2020 and if the rate of simple interest is 6%, on the following bases: (a) Exact simple interest (actual/actual) (b) Ordinary simple interest (30/360) (c) The Banker’s Rule (actual/360)

Answer 1

In same Simple Interest method, Interest can be calculated with following formula

$I = P\times i\times t$

where,

I = Interest amount

P = Principal (Initial deposit)

i = interest rate

t = time (deposit day to withdraw date)

We have following information -

P = $ 5,000

i = 6% simple interest

Deposit date = 08/27/2018

withdraw date = 05/04/2020

In order to calculate, we need to calculate Time (t) first. There are several method of day count conversion, we will explain below methods related to our questions.

1. Exact simple Interest (actual/actual) basis

It uses actual days between deposit date to withdraw date divided by actual date in a year.

Lets calculate the Time(t) for our question as per actual/actual basis.

Day count between 08/27/2018 - 05/04/2020 = 616 days

Actual average date between 2018,2019 & 2020 = (365+365+366)/3 = 365.3333

Thus, Time(t) = 616/365.333333 = 1.686131

Therefore, Interest (I) = 5000*0.06*1.686131

= $ 505.84

2. Ordinary simple interest (30/360) basis

It consider each month has 30 days and each has 360 days.

Lets calculate the Time(t) for our question as per 30/360 basis.

Day count between 08/27/2018 - 05/04/2020 if each month has 30 days = 607 days

Days in a year = 360

Thus, Time(t) = 607/360 = 1.6861111

Therefore, Interest (I) = 5000*0.06*1.68611111

= $ 505.83

3. The Banker's rule (actual/360)

It consider actual days between holding period and each year has 360 days.

Lets calculate the Time(t) for our question as per actual/actual basis.

Day count between 08/27/2018 - 05/04/2020 = 616 days

Days in a year = 360

Thus, Time(t) = 616/360 = 1.7111111

Therefore, Interest (I) = 5000*0.06*1.7111111

= $ 513.33

Please note- we can also calculate time in excel using "=yearfrac" formula.