Surbhi deposited 500 per month in a bank for 6 months in recurring deposit account. If the rate of interest
is 8% per annum and the interest is calculated at the end of month, then what will be the maturity value of
her deposits?
Answers
Answer:
How to use it
The maturity value of the deposit will depend on the amount of investment, duration of the deposit and the interest rate.
You will have to enter the date of opening of the FDRD, and then enter the amount of deposit which has to between Rs 500 and Rs 10 lakh. Thereafter, the duration has to be entered in months which have to be between 6 months and 120 months.
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Lastly, enter the annual rate of interest at which the recurring deposit investment has been made.
One can use the slider to put in different recurring deposit amounts to arrive at the final maturity value.
What it shows
On submitting the above information, the calculator will show the final maturity value of the investment. Based on the date of deposit and the tenure, the maturity date of the investment will also be shown. In addition, the break-up of maturity value, i.e., the investment amount and the interest earned will be shown separately.
How the result is arrived at
The formula used for arriving at the maturity value of a recurring deposit over a certain period at a certain interest rate is:
In case of recurring deposits, the compounding happens on quarterly basis.
The formula is: A = P*(1+R/N)^(Nt)
Here, A is the maturity amount in Rs., the recurring deposit amount is 'P' in Rs., 'N' is the compounding frequency, interest rate R in percentage and 't' is the tenure.
For a 12 month RD of Rs 5,000 at 8 percent per annum, the maturity value will be the sum of the series as below:
A = P*(1+R/N)^(Nt)
= 5000*(1+.0825/4)^(4*12/12) = 5425.44
= 5000*(1+.0825/4)^(4*11/12) = 5388.64
...
= 5000*(1+.0825/4)^(4*1/12) = 5034.14
Total maturity value ( sum of series) = Rs 62730.85
Given : Surbhi deposited 500 per month in a bank for 6 months in recurring deposit account.
rate of interest is 8% per annum
the interest is calculated at the end of month,
To Find : the maturity value of her deposits
Solution:
A = P (1 + R/100)ⁿ
P = 500 R = 8 % per annum = 2/3 % per month
n = from 6 to 1
Amount = 500 ( 1 + 2/300)⁶ + 500 ( 1 + 2/300)⁵ +____+ 500 ( 1 + 2/300)¹
a = 500 ( 1 + 2/300)
r = ( 1 + 2/300) = (151/150)
n = 6
Sₙ = a(rⁿ - 1) / ( r - 1)
= 500 ( 1 + 2/300) ((151/150)⁶ - 1) / (151/150 - 1) )
= 500 * 151 * (151/150)⁶ - 1)
= 3,070.78 Rs
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