A company has to redeem debentures of ` 10,00,000 at the end of 3 years from now. How much money should the company accumulate every year at 10% interest rate?
Question
A company has to redeem debentures of ` 10,00,000 at the end of 3 years from now. How much money should the company accumulate every year at 10% interest rate?
Solution
To solve this problem, we need to use the formula for the future value of an annuity, which is:
FV = P * [(1 + r)^n - 1] / r
Where: FV = Future Value (the total amount of money the company needs to accumulate, which is `10,00,000) P = Payment per period (the amount of money the company needs to accumulate each year, which we're trying to find) r = Interest rate per period (10% or 0.10) n = Number of periods (3 years)
We can rearrange the formula to solve for P:
P = FV * r / [(1 + r)^n - 1]
Substituting the given values:
P = 10,00,000 * 0.10 / [(1 + 0.10)^3 - 1]
P = 1,00,000 / [(1.10)^3 - 1]
P = 1,00,000 / [1.331 - 1]
P = 1,00,000 / 0.331
P = `3,02,115.71
So, the company should accumulate approximately 3,02,115.71 each year to be able to redeem the debentures of
10,00,000 at the end of 3 years at a 10% interest rate.
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