The time it takes for a man to get Rs 50,000 is 5 years and 4 months i.e., t = 5.36 years. Using the compound interest formula the required value is calculated.
<h3>What is the formula for calculating compound interest?</h3>
The formula for calculating the compound interest is
A = P(1 + r)^t
Where
A = total amount at the end of the tenure
P = Initial amount
r = Interest rate
t = time(years)
<h3>Calculation:</h3>
It is given that,
A man invested Rs 30,000; the rate of interest r = 10% and he gets a total amount of Rs 50,000 after some time 't'.
Then,
A = P(1 + r)^t
⇒ 50000 = 30000(1 + 0.1)^t
⇒ (1.1)^t = 50000/30000
⇒ (1.1)^t = 5/3 =1.67
Applying logarithm on both sides,
log(1.1)^t = log(1.67)
⇒ t (log(1.1) = log(1.67)
⇒ t = log(1.67)/log(1.1)
∴ t = 5.38 years
Therefore, it takes 5 years and 4 months to get the amount of Rs 50,000 for the initial investment of Rs 30,000.
Learn more about the compound interest here:
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