Mahesh plans to send his daughter for higher studies abroad after 10years. He expects the cost of these studies to be Rs. 10,00,000. Howmuch should he save at the beginning of each year to have a sum ofRs. 10,00,000 at the end of 10 years, if the interest rate is 10%compounded annually?
Question
Mahesh plans to send his daughter for higher studies abroad after 10years. He expects the cost of these studies to be Rs. 10,00,000. Howmuch should he save at the beginning of each year to have a sum ofRs. 10,00,000 at the end of 10 years, if the interest rate is 10%compounded annually?
Solution
To solve this problem, we need to use the formula for the future value of an ordinary annuity, which is:
FV = P * [(1 + r)^n - 1] / r
Where: FV = Future Value (the total amount of money you will have saved after n years) P = Payment (the amount of money you save each year) r = Interest rate (expressed as a decimal) n = Number of years
In this case, we know that FV = Rs. 10,00,000, r = 10% or 0.10, and n = 10 years. We need to find P.
Rearranging the formula to solve for P gives us:
P = FV * r / [(1 + r)^n - 1]
Substituting the known values into the formula gives us:
P = 10,00,000 * 0.10 / [(1 + 0.10)^10 - 1]
Solving this equation will give us the amount Mahesh needs to save at the beginning of each year.
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