house appreciation rate

Question

My parents bought a house for $250,000. If it appreciates in value (or gains value) at a rate of 4% per year, how many years will it take before their home is worth $325,000?

Answer 1

To solve this problem we use the equation A=P(1+r/n)^nt.

A is the final quantity.

P is the amount you started with.

r is the growth rate

t is the number of years

Here, A= 325,000, P=250,000, r=0.04, n=1 since the rate is only compounded once a year. Find t.

325,000=250,000(1+.04)^t

325,000/250,000=(1.04)^t

1.3=(1.04)^t; Take the natural logarithm of both sides, and apply the laws of logarithms.

ln(1.3) = ln((1.04)^t); Recall that ln(a^m)=m*ln(a).

ln(1.3)=t*ln(1.04)

ln(1.3) / ln(1.04)=t

t=6.69 years

Answer 2

325000 = 250000(1 + 0.04)^t

1.3 = 1.04^t

ln 1.3 = ln 1.04t

Can you solve for t and answer?