Mr. Rahul wants to invest Rs. 1,00,000 today. He is offered two investment options:
Option A: A fixed deposit that offers 8% annual interest compounded annually for 5 years.
Option B: A recurring deposit that offers Rs. 25,000 annually at the end of each year for 5 years with an interest rate of 8% p.a.
Which option should Mr. Rahul choose based on the concept of present value? Show your calculations.
Answer (2)
Mr. Rahul should choose Option A (Fixed Deposit), which yields approximately Rs. 146933 after 5 years, compared to Option B (Recurring Deposit) which yields approximately Rs. 146666. The fixed deposit offers a higher future value due to compound interest. Thus, investing in the fixed deposit is more beneficial.
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To determine which investment option Mr. Rahul should choose, we need to calculate the present value of both options.
Option A: Fixed Deposit
The fixed deposit offers 8% annual interest compounded annually for 5 years.
Using the formula for compound interest:
A = P ( 1 + r ) n
Where:
A is the amount after n years,
P is the principal amount (Rs. 1,00,000),
r is the annual interest rate (8% or 0.08), and
n is the number of years (5).
Plugging in the values:
A = 1 , 00 , 000 ( 1 + 0.08 ) 5 = 1 , 00 , 000 ( 1.4693 ) = R s .1 , 46 , 930
The future value of the fixed deposit after 5 years is Rs. 1,46,930.
Option B: Recurring Deposit
The recurring deposit offers Rs. 25,000 annually at the end of each year with an interest rate of 8% per annum.
To find the present value of these cash flows, we can use the Present Value of an Annuity formula:
P V = C × ( r 1 − ( 1 + r ) − n )
Where:
C is the annual cash flow (Rs. 25,000),
r is the annual interest rate (0.08), and
n is the number of years (5).
Plugging in the values:
P V = 25 , 000 × ( 0.08 1 − ( 1 + 0.08 ) − 5 )
P V = 25 , 000 × ( 0.08 1 − 0.6806 )
P V = 25 , 000 × 3.993 ≈ R s .99 , 825
Conclusion
Option A : Future Value of Rs. 1,46,930
Option B : Present Value of Rs. 99,825
Since Mr. Rahul should choose the option with the higher present value, Option A (Fixed Deposit) is the better choice as it offers a higher future value when compounded over 5 years. This means he will have more money at the end of the investment term with the fixed deposit.
