# Reinvestment Deposit Scheme

K. Sampath, Kanchipuram . 30 Apr 2020

## Reinvestment - Explanation of the word

The interest amount is calculated for every quarter and it is reinvested into the initial amount and compounded.

(Note: Since all banks in India calculate compound interest quarterly, this document is created accordingly.)

## The method of calculating compound interest

1. First calculate the simple interest for three months.

Formula for calculating simple interest is ->

i = (P * N * R)/100


Here
i = Interest amount
P = Amount(Investment amount)
N = Period(Number of Months)
R = Rate of Interest(Yearly)

Example,

Consider Amount P = Re 1
Period N = 3 Months
Rate of Interest R = 6 percent

Accordingly the simple interest for 3 months = (PNR)/100 = 1* 3/12* 6/100 = 0.015 (Rupees)

1. As calculated above the interest amount of Rs 0.015 is added to the original invested amount of Re 1 (1+0.015=1.015) and this new amount Rs 1.015 will be considered as invested amount for the next quarter.

As stated above interest on interest has to be gained, this method is called as reinvestment.

Now simple interest will be calculated for the next quarter for the above mentioned reinvested amount.

Interest amount(i) = PNR/100 (Where P=1.015, N=3 & R = 6%)
= 1.015* 3/12* 6/100
= 0.015225

If we now add this interest to the initial amount of Rs 1.015, we will receive the initial amount and compounded interest (ie maturity) at the end of 2 quarters.

Maturity amount = 1.015 + 0.015225 = Rs 1.030225

1. Thus the maturity amount can be calculated based on the original invested amount and the number of quarters it is invested for.
1. Instead of calculating maturity amount for each quarter, we can use the below formulae to get the final maturity amount directly

### Formula for Fixed Deposit Reinvestment

$Mv = [(P *N *R)+1]^{Q}$

Here
Mv = Maturity amount
P = Investment amount(1 Rupee)
N = Period - 3 months
R = Rate of Interest(Yearly)
Q = Number of Quarters

For example, If we have to calculate the maturity amount for 2 quarters at 6% rate of interest

Mv = [(1* 3/12 * 6/100)+1]2 = 1.030225 (Rupees)

For example, If we have to calculate the maturity amount for the investment amount of Rs. 15,000/- at 6% rate of interest for 3 years(ie 12 quarters)

Mv = 15000 * [(1 *3/12 *6/100)+1]12) = 17,934.27 (Rupees)

### Formula for monthly recurring deposit reinvestment plans

In this method, the investment is paid every month. To calculate the maturity amount for this plan, here we are going to follow the Discount factor method.

(Note: When the interest is calculated quarterly, the discount factor is used if the customer wants to receive interest on a monthly basis. We will see about the discount factor in another blog.)

### Formula for Discount Interest Factor

x = (P * R) / (1200+R)


Here,
x = Discount factor
P = Investment amount(1 Rupee)
R = Rate of interest(yearly)

### Formula for Maturity amount

Mvrd = ((x+1)(n+1) - (x+1)) / (x)

Here,
Mvrd = Maturity amount
x = Discount factor
n = Number of months

For example, If we have to calculate the maturity amount for the recurring monthly amount of Rs. 1,000/- at 6% rate of interest for 3 years(ie 12 quarters)

x = (1 * 6)/ (1200+6) = 0.0049751
Mvrd = 1000 * ((0.0049751+1) (12+1) - (0.0049751+1)) / (0.0049751)
= 1000 * 12.3952256
= 12,395.23 (Rupees)

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