Using the formula for compound interest with n compounding periods, how long (to the nearest tenth of a year) will it take for $12,500 to grow to $20,000 at 6.5% compounded quarterly?

Question

Use formula for compound interest

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the time it takes for the initial amount to turn into 20,000 after 4 years. Then, we have the formula such that

20,000 = 12,500(1+ .065/4)^4t

20000 = 12500(1.01625)^4t...............Then divide 12500 to both sides of the equal sign such that

1.6 = (1.01625)^4t..............Now take the natural log of both sides such that

ln(1.6) = 4tln(1.01625).............Now divide 4ln(1.01625) to both sides such that

ln(1.6) / (4*ln(1.01625)) = t ≈ 7.3 years

I hope this helped!