Find the number of years it will take for ​$37,000 to grow to ​$39,276.25 at 4​% interest compounded quarterly.

Answer 1

So the formula to know for these kind of problems is :

A = P(1 ± n/r)^rt

A: Final amount

P: Starting amount

n: Rate of growth/decay (the ± is + for growth and - for decay)

r: Rate of compounding (if it's 2 times per year this number is 2, if its every month per year its 12)

t: Time elapsed

So you could plug this problem into that formula to get:

39,276.25 = 37,000 (1 + 0.04/4)^4t

Now we have to solve for t, 1st divide both sides by 37,000 to get:

39,276.25 / 37,000 = (1.01)^4t

Now we take the log of both sides to remove t from the exponent:

log(39,276.25 / 37,000) = 4 * t * log(1.01)

log(39,276.25 / 37,000) / 4 = t * log(1.01)

log(39,276.25 / 37,000) / (4 * log(1.01)) = t

After plugging these numbers into a calculator, you can solve for t as 1.5 years.

Hope this helped!

Answer 2

39276.25 = 37000(1 + 0.04/4)^4t

39726.25 = 37000(1.01)^4t

ln 39726.25 = 4t ln 37000

5.998 ≈ 4t

1.4995 ≈ t