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Compound interest on certain sum of money at rate of 10% for 2⅓ years is 1201.60 compounded yearly. Find the sum.?
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Compound interest on certain sum of money at rate of 10% for 2⅓ years ...
Given:
- Rate of interest = 10%
- Time = 2⅓ years = 2 + 1/3 years = 2 + 1/3 * 12 months = 2 + 4 months = 2 + 4/12 years = 2 + 1/3 years = 2.3333 years
- Compound interest = $1201.60 compounded yearly

To find:
- The principal sum (initial amount)

Formula:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)

Where:
A = Final amount (including principal and interest)
P = Principal amount (initial amount)
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Time (in years)

Calculation:
Let's assume the principal sum is P.

Substituting the given values into the formula, we have:
A = P(1 + r/n)^(nt)
1201.60 = P(1 + 0.10/1)^(1 * 2.3333)
1201.60 = P(1 + 0.10)^(2.3333)
1201.60 = P(1.10)^(2.3333)

Simplifying the equation, we take the cube root of both sides to isolate the principal amount:
(1.10)^(2.3333) = 1.10^2 * 1.10^(1/3)
1.10^(2.3333) = 1.21 * 1.10^(1/3)

Taking the cube root of both sides:
1.10^(2.3333/3) ≈ 1.10^(0.7778)
1.10^(0.7778) ≈ 1.2114

Now we can solve for P:
1201.60 = P * 1.2114

Dividing both sides by 1.2114:
P ≈ 1201.60 / 1.2114
P ≈ 991.58

Therefore, the principal sum (initial amount) is approximately $991.58.
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Compound interest on certain sum of money at rate of 10% for 2⅓ years is 1201.60 compounded yearly. Find the sum.?
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