Answer: It takes 0.0189 years or 6.9340 days for $56 billion invested at an effective rate of 7.4% to earn an interest of $76 million.
We arrive at the answer as follows
We have
Bill Gates’ estimated net worth in 2009 = $56 billion or 56,000 million
Effective Rate of interest earned = 7.4%
Interest earned = $76 million
Let Bill Gates’ estimated net worth in 2009 be Present Value or PV
Let Bill Gates’ income after earning an interest of $76 million be Future Value or FV
Now, FV is nothing but principal invested and the interest earned during the period of investment.
So,

Now we take a look at the FV formula with respect to time value of money. In this case,

Substituting the values we have in the formula above, we get,


-------- (1)
At this stage we can use log to the base 10 in order to find n.
When we convert an exponent into a log, it becomes exponent times that number. For. eg.
becomes
.
So, we can rewrite (1) above as

Substituting the log₁₀ values in the equation above we get


Since n is less than one year, we can express it in days by multiplying the answer above with 365.
We get,
0.018997378 * 365 = 6.934043124 days