Ramesh plans to save some amount required after 10 years for higher studies of his son. He expects the cost of these studies to be Rs.1,00,000. How much should he save at the beginning of each year to accumulate this amount at the end of 10 years, if the interest rate is 12% compounded annually. (Given $(1.12)^{11}=3.477$)

Ramesh wants to save money for his son's education that will cost Rs. 1,00,000 after 10 years. He will deposit an equal amount at the beginning of each year for 10 years with 12% interest compounded annually.

Since Ramesh saves at the beginning of each year (not at the end), this is an Annuity Due.

💡 In an Ordinary Annuity, payments are made at the end of each period. In an Annuity Due, payments are made at the beginning — so every payment earns one extra year of interest.

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The Future Value formula for an Annuity Due is:

$FV = P \times \dfrac{(1+r)^n - 1}{r} \times (1+r)$

where:

• $FV$ = Future Value needed $= Rs. \text{ } 1,00,000$
• $P$ = Annual payment (to find)
• $r$ = Interest rate $= 12\% = 0.12$
• $n$ = Number of years $= 10$

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Let's combine the $(1+r)$ terms in the formula to make it easier to use the given hint:

$FV = P \times \dfrac{(1+r)^{n+1} - (1+r)}{r}$

Plugging in $n = 10$ and $r = 0.12$:

$1,00,000 = P \times \dfrac{(1.12)^{11} - 1.12}{0.12}$

💡 Notice the formula needs $(1.12)^{11}$, which is exactly the value given in the question: $(1.12)^{11} = 3.477$

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Substituting:

$1,00,000 = P \times \dfrac{3.477 - 1.12}{0.12}$

$= P \times \dfrac{2.357}{0.12}$

$= P \times 19.6416$

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Solving for $P$:

$P = \dfrac{1,00,000}{19.6416}$

$P \approx Rs. \text{ } 5,091.27$

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Therefore, Ramesh should save approximately $Rs. \text{ } 5,091$ at the beginning of each year to accumulate $Rs. \text{ } 1,00,000$ at the end of 10 years at $12\%$ interest compounded annually.