Your Father Committed To Present You With A Car For Your Graduation After 7 Years From Now

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Your father committed to present you with a car for your graduation after 7 years from now. The car will cost Tk. 35,00,000 at the time. Your father is planning to accumulate the fund by depositing an equal amount of money in a bank account b earning 13% interest. How much is in the bank account Assume that deposit should your father deposit in the bank account? Assume that the deposit should be made at the beginning of the period. If the deposit is made at the end of the period then what will the amount of the deposit be?

To determine the required annual deposit, we calculate the annual payment () needed to reach a future goal of Tk. 35,00,000 in 7 years at an interest rate of 13%.

Given Information

Target Future Value (): Tk. 35,00,000
Interest Rate (): 13% or
Time Period (): 7 years

Part 1: Deposit Made at the Beginning of Each Period (Annuity Due)

When deposits are made at the beginning of each year, the money earns interest for an extra compounding period. We use the Future Value of an Annuity Due formula:

Where:

Now, solving for the annual payment ():

If your father makes the deposit at the beginning of each year, he needs to deposit Tk. 2,97,688.33 annually.

Part 2: Deposit Made at the End of Each Period (Ordinary Annuity)

When deposits are made at the end of each year, we use the standard Future Value of an Ordinary Annuity formula:

Solving for :

If your father makes the deposit at the end of each year, he needs to deposit Tk. 3,36,387.81 annually.

Comparison Summary

Deposit Timing	Type of Annuity	FVIFA Factor	Annual Deposit Required (Tk.)	Total Deposited (7 Yrs)	Total Interest Earned (Tk.)
Beginning of Year	Annuity Due	11.757263	2,97,688.33	20,83,818.31	14,16,181.69
End of Year	Ordinary Annuity	10.404658	3,36,387.81	23,54,714.67	11,45,285.33

Key Takeaway: Depositing at the beginning of each year saves Tk. 38,699.48 annually (a total savings of Tk. 2,70,896.36 in out-of-pocket deposits) because each payment compounds for one additional year.

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