WILL GIVE BRAINLIEST Mr. and Mrs. Bailey hope to send their son to college in eleven years. How much money should they invest no
1 answer:
Mr. and Mrs. Bailey need to invest $2906.50 so as to send their son to college.
<h3>Compound interest</h3>Compound interest is given by:
where A is the amount after t years, P is initial amount, r is the rate and n is the times compounded per period
Given that n = 1, r = 9% = 0.09, A = $7500 t = 11. Hence:
Mr. and Mrs. Bailey need to invest $2906.50 so as to send their son to college.
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Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus: