A sum of money was invested for 3 years at the rate of 4% per annum compounded annually amounted to $84,364.80. what is the sum invested?
Answers
Given : A sum of money was invested for 3 years at the rate of 4% per annum compounded annually amounted to $84,364.80.
To Find : what is the sum invested?
Solution:
A = P (1 + R/100)ⁿ
A = $84,364.80
P = ?
R = 4
n = 3
=> 84,364.80 = P (1 + 4/100)³
=> 84,364.80 = P (1.04)³
=> 84,364.80 = P (1.124864)
=> P = 75,000
Sum invested = $ 75000
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Solution :-
Let us assume that, the sum invested was $P .
we know that, when rate is compounded annually,
- A = P[1 + (R/100)]^T
we have,
- A = $84,364.80
- T = 3 years.
- R = 4 % per annum .
so, putting all values we get,
→ 84364.8 = P[1 + (4/100)]³
→ 84364.8 = P[1 + (1/25)]³
→ 84364.8 = P(26/25)³
→ P = (84364.8 * 25 * 25 * 25) / (26 * 26 * 26)
→ P = $75000 (Ans.)
Hence, the sum invested was $75000 .
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