Find the time required for an investment of 5000 dollars to grow to 8500 dollars at an interest rate of 7.5 pe? and Fail-Safe Venture Investment

Find the time required for an investment of 5000 dollars to grow to 8500 dollars at an interest rate of 7.5 pe?

Find the time required for an investment of 5000 dollars to grow to 8500 dollars at an interest rate of 7.5 percent per year, compounded quarterly.


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Answer by θ βяιαη θ
Recall your compound interest formula.

A = P(1 + r/n)^(nt)

Since the rate is 7.5%/year, we have that r = 0.075. Also, we are compounding 4 times a year. So we have that n = 4. We are also given that A = 8500 and P = 5000. So we have:

8500 = 5000(1 + 0.075/4)^(4t)
==> 8500 = 5000(1.01875)^(4t)
==> 1.7 = 1.01875^(4t)
==> ln(1.7) = ln[1.01875^(4t)]
==> ln(1.7) * 4t*ln(1.01875)
==> 4t = ln(1.7)/ln(1.01875)
==> t = ln(1.7)/[4ln(1.01875)] ≈ 7.14

So it will take about 7.14 years.

I hope this helps!

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