Question

A newly couple has $15,000 toward the purchase of a house. For the type and size of house the couple is interested in buying, an estimated down payment of $20,000 will be necessary. How long will the money have to be invested at 10% compounded quarterly to grow to $20,000?


This is what I have so far
A=P(1+r/n)^(n*t)
20,000 = 15,000 (1+0.1/4)^(4*t)
divide both sides by 15,000
4/3 = (1 + 0.1/4)^(4*t)
4/3 = 1.025^(4*t)

Now I'm stuck and don't know if should take the natural logs

Answer 1

log 4/3 = log [1.025^(4*t)]
log 4/3 = 4*t log 1.025
Divide both sides by log 1.025
solve for t

Answer 2

P = Po(1+r)^n = 20,000.

r = 0.1/yr * 0.25yr. = 0.025 = Quarterly % rate expressed as a decimal.

n = 4Comp/yr * t yrs. = 4t.

15,000(1.025)^4t = 20,000.
(1.025)^4t = 20,000/15,000 = 1.333,
4t*Log1.025 = Log1.333.
4t = Log1.333/Log1.025 = 11.7,
t = 2.91 Yrs.