The amount of money in the account every year, when ` 10000 is deposited atcompound interest at 8 % per annum.
Question
The amount of money in the account every year, when ` 10000 is deposited atcompound interest at 8 % per annum.
Solution
The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Given in the problem:
- P = 10000
- r = 8% or 0.08 (in decimal)
- n = 1 (since it's compounded annually)
- t = 1 year (since we're looking for the amount every year)
Let's calculate the amount after 1 year:
A = 10000(1 + 0.08/1)^(1*1) = 10000(1 + 0.08)^1 = 10000 * 1.08 = 10800
So, after 1 year, the amount in the account will be ` 10800.
For the next years, you just need to replace t with the respective year and calculate the amount. For example, for the 2nd year, t = 2:
A = 10000(1 + 0.08/1)^(1*2) = 10000(1 + 0.08)^2 = 10000 * 1.08^2 = 11664
So, after 2 years, the amount in the account will be ` 11664.
You can continue this process for as many years as you want to know the amount in the account.
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